{"id":31750,"date":"2023-07-12T09:56:12","date_gmt":"2023-07-12T09:56:12","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=31750"},"modified":"2023-07-12T15:26:48","modified_gmt":"2023-07-12T15:26:48","slug":"multiplying-polynomials-definition-steps-methods-examples-facts","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplying-polynomials","title":{"rendered":"Multiplying Polynomials: Definition, Steps, Methods, Examples, Facts"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-e5095090-1008-4b2a-ab2e-5b83fb31dfa7\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplying-polynomials#0-what-is-the-multiplication-of-polynomials>What Is the Multiplication of Polynomials?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplying-polynomials#1-rules-for-multiplying-polynomials>Rules for Multiplying Polynomials<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplying-polynomials#3-multiplying-polynomials-with-different-or-mixed-variables>Multiplying Polynomials with Different or Mixed Variables<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplying-polynomials#12-solved-examples-on-multiplying-polynomials>Solved Examples on Multiplying Polynomials<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplying-polynomials#13-practice-problems-on-multiplying-polynomials>Practice Problems on Multiplying Polynomials<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplying-polynomials#14-frequently-asked-questions-on-multiplying-polynomials>Frequently Asked Questions on Multiplying Polynomials<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-multiplication-of-polynomials\">What Is the Multiplication of Polynomials?<\/h2>\n\n\n\n<p>To multiply two polynomials, we use the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/distributive-property\">distributive property<\/a> of multiplication where we multiply each <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/term\">term<\/a> of the first polynomial by each term of the second polynomial. While doing so, we multiply variables with variables, coefficients with coefficients, and finally add all the results together.<\/p>\n\n\n\n<p>There are different <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/types-of-polynomials\">types of polynomials<\/a> based on the number of terms, such as monomials, binomials, trinomials, and so on. We use different strategies to multiply different types of polynomials together.&nbsp;<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-solution-by-multiplying-by-hundreds-and-thousands\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_multi_by_tens_4d_1d_pv_pt.png\" alt=\"Complete the Solution by Multiplying by Hundreds and Thousands Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Solution by Multiplying by Hundreds and Thousands Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-solution-by-multiplying-by-hundreds\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_multi_by_tens_3d_1d_pv_pt.png\" alt=\"Complete the Solution by Multiplying by Hundreds Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Solution by Multiplying by Hundreds Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-solution-by-multiplying-by-ones-and-tens\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_mult_by_ones_3d_1d_pv_pt.png\" alt=\"Complete the Solution by Multiplying by Ones and Tens Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Solution by Multiplying by Ones and Tens Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-solution-by-multiplying-by-ones\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_mult_by_ones_pv_pt.png\" alt=\"Complete the Solution by Multiplying by Ones Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Solution by Multiplying by Ones Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-solution-by-multiplying-by-tens\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_multi_by_tens_pv_pt.png\" alt=\"Complete the Solution by Multiplying by Tens Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Solution by Multiplying by Tens Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-area-by-multiplying-side-lengths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_multi_side_length_1_pt.png\" alt=\"Find Area by Multiplying Side Lengths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Area by Multiplying Side Lengths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-out-the-total-money-spent-by-multiplying\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/measurement_mul_word_prob_2_pt.png\" alt=\"Find Out the Total Money Spent by Multiplying Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Out the Total Money Spent by Multiplying Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-area-by-multiplying-the-side-lengths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_multiply_pt.png\" alt=\"Find the Area by Multiplying the Side Lengths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Area by Multiplying the Side Lengths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-the-product-by-multiplying-two-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_mult_by_ones_2d_2d_pv_pt.png\" alt=\"Find the Product by Multiplying Two Digit Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find the Product by Multiplying Two Digit Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/understand-decimal-point-placement-by-multiplying\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/dec_mul_div_placement_of_dec_point_1_pt.png\" alt=\"Understand Decimal point Placement by Multiplying Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Understand Decimal point Placement by Multiplying Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-rules-for-multiplying-polynomials\">Rules for Multiplying Polynomials<\/h2>\n\n\n\n<p>In the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication\">multiplication<\/a> of polynomials, the polynomials can be monomials, binomials, trinomials, etc. The steps to multiply two or more polynomials are as follows:<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> If any one of the polynomials contains more than one term, then first apply the distributive law of multiplication to multiply each term in one polynomial by each term in the other polynomial.<\/p>\n\n\n\n<p><strong>Step 2: <\/strong>Using the laws of exponents, add the powers of the same variables.<\/p>\n\n\n\n<p><strong>Step 3: <\/strong>Add or subtract the like terms and then simplify to get the final results.<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/equivalent-fractions-by-multiplying-or-dividing\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/equivalent-fractions-by-multiplying-or-dividing.jpeg\" alt=\"Equivalent Fractions by Multiplying or Dividing Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/multiplying-decimals-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/multiplying-decimals-numbers.jpeg\" alt=\"Multiplying Decimals Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/multiplying-decimals-using-standard-algorithm\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/multiplying-decimals-using-standard-algorithm.jpeg\" alt=\"Multiplying Decimals Using Standard Algorithm Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/multiplying-fractions-by-mixed-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/multiplying-fractions-by-mixed-numbers.jpeg\" alt=\"Multiplying Fractions by Mixed Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/multiplying-mixed-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/multiplying-mixed-numbers.jpeg\" alt=\"Multiplying Mixed Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/multiplying-non-unit-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/multiplying-non-unit-fractions.jpeg\" alt=\"Multiplying Non Unit Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/multiplying-unit-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/multiplying-unit-fractions.jpeg\" alt=\"Multiplying Unit Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/multiplying-using-arrays\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/multiplying-using-arrays.jpeg\" alt=\"Multiplying Using Arrays Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/multiplying-using-equal-groups\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/multiplying-using-equal-groups.jpeg\" alt=\"Multiplying Using Equal groups Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/multiplying-whole-numbers-by-decimals\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/multiplying-whole-numbers-by-decimals.jpeg\" alt=\"Multiplying Whole Numbers by Decimals Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-multiplying-polynomials-using-exponents-law\">Multiplying Polynomials using Exponents Law<\/h2>\n\n\n\n<p>When we multiply two terms in which the same variables are present, we use the laws of exponents.<\/p>\n\n\n\n<p><strong>a<\/strong><strong><sup>m&nbsp; <\/sup><\/strong><strong>\u00d7<\/strong><strong> a<\/strong><strong><sup>n<\/sup><\/strong><strong> = a<\/strong><strong><sup>m + n<\/sup><\/strong><\/p>\n\n\n\n<p>Note that we multiply the coefficients of the variables separately.&nbsp;<\/p>\n\n\n\n<p><strong>Example: <\/strong>$11 x^{2} \\times 2x^{5} = 22x^{7}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-multiplying-polynomials-with-different-or-mixed-variables\">Multiplying Polynomials with Different or Mixed Variables<\/h2>\n\n\n\n<p>It is not necessary that the polynomials being multiplied should be in the same variable. If the two polynomials have different or mixed variables, we use the following rules.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiply all the coefficients.&nbsp;<\/li>\n\n\n\n<li>Apply the exponent rules when multiplying the same variables.<\/li>\n\n\n\n<li>Other variables are simply multiplied together in the answer.<\/li>\n<\/ul>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>$4x^{2}\\;y \\times 3yz = 12x^{2}\\;y^{2}\\;z$<\/p>\n\n\n\n<p>$2x \\times (\\;-\\; 5)xy \\times 7z = \\;-\\; 70x^{2}\\;yz$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-how-to-multiply-polynomials\">How To Multiply Polynomials<\/h2>\n\n\n\n<p>To learn how to multiply polynomials, we will discuss different categories, such as<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiplying monomials<\/li>\n\n\n\n<li>Multiplying binomials<\/li>\n\n\n\n<li>Multiplying a monomial and a binomial<\/li>\n\n\n\n<li>Multiplying a binomial and a trinomial<\/li>\n<\/ul>\n\n\n\n<p>This way it will be easier to understand how to approach different types of problems involving multiplying polynomials. Let\u2019s discuss these cases in detail.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-multiplication-of-monomials\">Multiplication of Monomials<\/h2>\n\n\n\n<p><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/monomial\">Monomial<\/a> is a polynomial containing only one term. This term can be a constant, a variable with a coefficient or a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/product\">product<\/a> of one or more variables with a coefficient.<\/p>\n\n\n\n<p><strong>Multiplication of Two Monomials<\/strong><\/p>\n\n\n\n<p>Here, we just have to multiply the single term of the first monomial by the single term of the other monomial. Multiply variables with variables, coefficients with coefficients, and combine the result. If both the monomials have the same variable then their exponents are added together.<\/p>\n\n\n\n<p><strong>Examples:<\/strong>&nbsp;<\/p>\n\n\n\n<p>$4x \\times 5x = (4 \\times 5) \\times (x \\times x) = 20x^{1+1} = 20x^{2}$<\/p>\n\n\n\n<p>$8xy \\times 7xy^{2} = (8 \\times 7) \\times (x \\times x) \\times (y \\times y^{2}) = 56\\; x^{2}\\;y^{3}$<\/p>\n\n\n\n<p><strong>Multiplication of Three Monomials<\/strong><\/p>\n\n\n\n<p>Here, we multiply three terms together. We can multiply three monomials by applying the same method as multiplying two monomials.<\/p>\n\n\n\n<p><strong>Examples:<\/strong><\/p>\n\n\n\n<p>$4x \\times 5x \\times 6x = (4 \\times 5 \\times 6) \\times (x \\times x \\times x) = 120x^{1+1+1} = 120x^{3}$<\/p>\n\n\n\n<p>$x \\times 6xy \\times xyz = (1 \\times 6)(x \\times x \\times x) \\times z = 6x^{3}\\;y^{2}\\;z$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-multiplication-of-binomials\">Multiplication of Binomials<\/h2>\n\n\n\n<p>A binomial is a polynomial with only two terms. To multiply binomials, we use the distributive property of multiplication. We first multiply the first term of the first binomial by each term of the second binomial. Next, we multiply the second term of the first binomial by each term of the second binomial. Finally, we combine all the results using the operators.<\/p>\n\n\n\n<p>The mnemonic FOIL can be used to remember and understand the pattern used in the multiplying binomials.<\/p>\n\n\n\n<p>F: First terms&nbsp;<\/p>\n\n\n\n<p>O: Outer terms&nbsp;<\/p>\n\n\n\n<p>I: Inner terms&nbsp;<\/p>\n\n\n\n<p>L: Last terms<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"418\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/foil-for-multiplying-binomials.png\" alt=\"FOIL method - binomial multiplication mnemonic trick\" class=\"wp-image-31757\" title=\"FOIL method - binomial multiplication mnemonic trick\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/foil-for-multiplying-binomials.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/foil-for-multiplying-binomials-300x202.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Multiplying Binomials Using Distributive Property<\/strong><\/p>\n\n\n\n<p>Multiplication of a binomial $(a + b)$ with a binomial $(c + d)$ can be given as<\/p>\n\n\n\n<p>$(a + b) \\times (c + d) =  a \\times (c + d) + b \\times (c + d)$<\/p>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; $= ac + ad + bc + bd$<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>$(x \\;-\\; 2y ) \\times (x^{3} + yz) = x(x^{3} + yz) \\;-\\; 2y(x^{3} + yz)$<\/p>\n\n\n\n<p>$ = x^{4} + xyz \\;-\\; 2x^{3}\\;y\\;-\\;2y^{2}\\;z$<\/p>\n\n\n\n<p><strong>Multiplying Binomials Using the Box Method<\/strong><\/p>\n\n\n\n<p>We can multiply two binomials using the box method. Write the individual terms of two binomials along the rows and columns of a 22 box. Every cell contains the product of the terms it represents along the row and the column. Add all the products together to get the final result.<\/p>\n\n\n\n<p><strong>Example: <\/strong>(<strong>x<\/strong>&#8211;<strong>2)<\/strong>(y+xz)<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-regular\"><table class=\"wj-table-class\"><tbody><tr><td><\/td><td><strong>x<\/strong><\/td><td>$\\;-\\;2$<\/td><\/tr><tr><td><strong>y<\/strong><\/td><td>xy<\/td><td>$\\;-\\;2y$<\/td><\/tr><tr><td><strong>x<\/strong><strong>z<\/strong><\/td><td>x2z<\/td><td>$\\;-\\;2xz$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>$(x \\;-\\; 2)(y + xz) = x^{2}\\;z + xy \\;-\\; 2xz \\;-\\; 2y$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-how-to-multiply-a-monomial-with-a-binomial\">How to Multiply a Monomial with a Binomial<\/h2>\n\n\n\n<p>To multiply a monomial with a binomial use the distributive property of multiplication.<\/p>\n\n\n\n<p>Multiplication of a monomial <strong>a<\/strong> with a binomial $(b + c)$ can be given as<\/p>\n\n\n\n<p>$a(b + c) = (a \\times b) + (a \\times c)$<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>$2x \\times (x + y) = 2x \\times x + 2x \\times y = 2x^{2} + 2xy$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-how-to-multiply-binomial-with-a-trinomial\">How to Multiply Binomial with a Trinomial<\/h2>\n\n\n\n<p>A binomial <strong>(m + n<\/strong>) can be multiplied with a trinomial $(a + b + c)$ as<\/p>\n\n\n\n<p>$(m + n) \\times (a + b + c) = \\left[m (a + b + c)\\right] + \\left[n (a + b + c)\\right]$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= am + bm + cm +&nbsp; an + bn + cn$<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>$2xy \\times (x + 5y + z) = 2x^{2}\\;y + 2xyz$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-polynomial-long-multiplication\">Polynomial Long Multiplication<\/h2>\n\n\n\n<p>The horizontal multiplication method is convenient to use when we are dealing with small polynomials. However, if we wish to multiply polynomials having three or more terms, we can prefer the long multiplication method. It is exactly the same as the method of <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/long-multiplication\">long multiplication<\/a> for numbers.<\/p>\n\n\n\n<p>Let\u2019s understand with an example.<\/p>\n\n\n\n<p><strong>Example:<\/strong> $(y^{2} + 2y \\;-\\; 1) \\times (y + 5)$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"475\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/multiplying-polynomials-vertically.png\" alt=\"long multiplication of polynomials\" class=\"wp-image-31758\" title=\"long multiplication of polynomials\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/multiplying-polynomials-vertically.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/multiplying-polynomials-vertically-300x230.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-facts-about-multiplying-polynomials\">Facts about Multiplying Polynomials<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>Multiplication of polynomials follows <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/commutative-property\">commutative property<\/a> as well as <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property\">associative property<\/a>.<\/li>\n\n\n\n<li>The degree of the product of two or more polynomials with one variable is less than or equal to the sum of the degrees of each polynomial.<\/li>\n\n\n\n<li>A variable without exponent in a polynomial is said to have exponent 1.&nbsp;$x = x^{1}$<\/li>\n\n\n\n<li>If you multiply a polynomial with a non-zero constant, the degree of the polynomial will not be affected.<\/li>\n\n\n\n<li>Multiplying polynomials requires careful attention to the signs of the terms.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we have discussed the multiplication of polynomials with the help of different cases. Let\u2019s solve a few examples and practice problems to recall and revise these concepts.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-solved-examples-on-multiplying-polynomials\">Solved Examples on Multiplying Polynomials<\/h2>\n\n\n\n<p><strong>1. Find the product of <\/strong>$4x$<strong> and <\/strong>$9x$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>We have to multiply two monomials $4x$<strong> <\/strong>and<strong> <\/strong>$9x$.<\/p>\n\n\n\n<p>Required product $=4x \\times 9x$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=(4 \\times 9)x^{1+1}$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=36x^{2}$<\/p>\n\n\n\n<p><strong>2. Find the product of <\/strong>$p$<strong>, <\/strong>$3p$<strong>, and <\/strong>$5p + q$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>$p \\times 3p \\times (5p + q) = 3 \\times 5 \\times p \\times p \\times (5p + q)$<\/p>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; &nbsp; $=15p^{2} \\times (5p + q)$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= (15p^{2} \\times 5p) + (15p^{2} + q)$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 75p^{3} + 15p^{2} \\;q$<\/p>\n\n\n\n<p><strong>3. Multiply the two binomials: <\/strong>$(x^{2} + 7x)(x + 1)$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Verify the answer using the box method.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>$(x^{2} + 7x)(x + 1) = x^{2}(x + 1) + 7x (x + 1)$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= x^{3} + x^{2} + 7x^{2} + 7x$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= x^{3} + 8&#215;2 + 7x$<\/p>\n\n\n\n<p><strong>Box method:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td><\/td><td>$x^{2}$<\/td><td>7x<\/td><\/tr><tr><td><strong>x<\/strong><\/td><td>$x^{3}$<\/td><td>$7x^{2}$<\/td><\/tr><tr><td><strong>1<\/strong><\/td><td>$x^{2}$<\/td><td>7x<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>$\\bigg(x^{2} + 7x \\bigg)(x +1) = x^{3} + x^{2} + 7x^{2} + 7x = x^{3} + 8x^{2}$<\/p>\n\n\n\n<p><strong>4. Find the product of y and <\/strong>$(3y + 2)$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let\u2019s multiply the monomial y and binomial<strong> <\/strong>$(3y + 2)$.<\/p>\n\n\n\n<p>Required product $= y(3y + 2) = (3y \\times y) + 2y = 3y^{2} + 2y$<\/p>\n\n\n\n<p><strong>5. Find the product of <\/strong>$(x + 1)$<strong> and <\/strong>$(x + 4)$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Required product $= (x + 1)(x + 4)$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=x (x + 4) + 1(x + 4)$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=x \\times x + 4x + x + 4$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= x^{2} + 5x + 4$<\/p>\n\n\n\n<p><strong>6. Multiply <\/strong>$(2x^{2} + 5)(x^{2} \\;-\\; 3x + 2)$<strong> using long multiplication.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"309\" height=\"184\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/multiplying-polynomials-vertical-method.png\" alt=\"Long multiplication of polynomials\" class=\"wp-image-31759\" title=\"Long multiplication of polynomials\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/multiplying-polynomials-vertical-method.png 309w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/multiplying-polynomials-vertical-method-300x179.png 300w\" sizes=\"auto, (max-width: 309px) 100vw, 309px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-practice-problems-on-multiplying-polynomials\">Practice Problems on Multiplying Polynomials<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Multiplying Polynomials: Definition, Steps, Methods, Examples, Facts<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the product of $4t^{2}$ and $7^{t}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">28t<\/div><div class=\"spq_answer_block\" data-value=\"1\">$28t^{3}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$82t^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$28t^{2}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $28t^{3}$<br\/>Required product $=4t^{2} \\times 7t = 4 \\times 7 \\times t^{2} \\times t = 28t^{3}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the product of x  and $(x \\;\u2013\\; 3)$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$x^{2} \\;\u2013\\; 3$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$x^{2} + 3x$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$x^{2} \\;-\\; 3x$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$x^{2} \\;-\\; 9x$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $x^{2} \\;-\\; 3x$<br\/>Required product $= x(x \\;\u2013\\; 3) = x^{2} \\;-\\; 3x$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">What is the coefficient of the product of $5x^{2},\\; 4y$, and $2y$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">20<\/div><div class=\"spq_answer_block\" data-value=\"1\">40<\/div><div class=\"spq_answer_block\" data-value=\"2\">50<\/div><div class=\"spq_answer_block\" data-value=\"3\">80<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 40<br\/>$5x^{2} \\times 4y \\times 2y = (5 \\times 4 \\times 2)(x^{2} \\times y \\times y) = 40x^{2}\\;y^{2}$<br>\r\nHence, the coefficient of the product of $5x^{2},\\; 4y$ and 2y is 40.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">What is the product of $(2x \\;\u2013\\; 1)(3x + 4)$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$6x^{2} + 8x \\;\u2013\\; 1$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$6x^{2} + 5x \\;\u2013\\; 4$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$6x^{2} + 2x \\;\u2013\\; 4$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$6x^{2} + x \\;\u2013\\; 4$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $6x^{2} + 5x \\;\u2013\\; 4$<br\/>$(2x \\;\u2013\\; 1)(3x + 4)$<br>\r\n$= 6x^{2} + 8x \\;\u2013\\; 3x \\;\u2013\\; 4$<br>\r\n$= 6x^{2} + 5x \\;\u2013\\; 4$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The product of $(l + 3m)$ and $(l\\;-\\;2m)$ is equal to:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$l^{2} + ml \\;-\\; 6m^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$l^{2} + 3ml + 8m^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$2l^{2} \\;-\\; ml \\;-\\; m^{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$l^{2} + 5ml + 5m^{2}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $l^{2} + ml \\;-\\; 6m^{2}$<br\/>Required product $= (l + 3m) (l \\;-\\; 2m)$<br>\r\n                 $= l^{2} \\;-\\; 2ml + 3ml \\;-\\; 6m^{2}$<br>\r\n                 $= l^{2} + ml \\;-\\; 6m^{2}$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Multiplying Polynomials: Definition, Steps, Methods, Examples, Facts\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Multiplying Polynomials\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the product of $$4t^{2}$$ and $$7^{t}$$?\",\n                    \"text\": \"What is the product of $$4t^{2}$$ and $$7^{t}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Required product $$=4t^{2} \\\\times 7t = 4 \\\\times 7 \\\\times t^{2} \\\\times t = 28t^{3}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"28t\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Required product $$=4t^{2} \\\\times 7t = 4 \\\\times 7 \\\\times t^{2} \\\\times t = 28t^{3}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$82t^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Required product $$=4t^{2} \\\\times 7t = 4 \\\\times 7 \\\\times t^{2} \\\\times t = 28t^{3}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$28t^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Required product $$=4t^{2} \\\\times 7t = 4 \\\\times 7 \\\\times t^{2} \\\\times t = 28t^{3}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$28t^{3}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Required product $$=4t^{2} \\\\times 7t = 4 \\\\times 7 \\\\times t^{2} \\\\times t = 28t^{3}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Required product $$=4t^{2} \\\\times 7t = 4 \\\\times 7 \\\\times t^{2} \\\\times t = 28t^{3}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the product of x  and $$(x \\\\;\u2013\\\\; 3)$$?\",\n                    \"text\": \"What is the product of x  and $$(x \\\\;\u2013\\\\; 3)$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Required product $$= x(x \\\\;\u2013\\\\; 3) = x^{2} \\\\;-\\\\; 3x$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x^{2} \\\\;\u2013\\\\; 3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Required product $$= x(x \\\\;\u2013\\\\; 3) = x^{2} \\\\;-\\\\; 3x$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x^{2} + 3x$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Required product $$= x(x \\\\;\u2013\\\\; 3) = x^{2} \\\\;-\\\\; 3x$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x^{2} \\\\;-\\\\; 9x$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Required product $$= x(x \\\\;\u2013\\\\; 3) = x^{2} \\\\;-\\\\; 3x$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$x^{2} \\\\;-\\\\; 3x$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Required product $$= x(x \\\\;\u2013\\\\; 3) = x^{2} \\\\;-\\\\; 3x$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Required product $$= x(x \\\\;\u2013\\\\; 3) = x^{2} \\\\;-\\\\; 3x$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the coefficient of the product of $$5x^{2},\\\\; 4y$$, and $$2y$$?\",\n                    \"text\": \"What is the coefficient of the product of $$5x^{2},\\\\; 4y$$, and $$2y$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$5x^{2} \\\\times 4y \\\\times 2y = (5 \\\\times 4 \\\\times 2)(x^{2} \\\\times y \\\\times y) = 40x^{2}\\\\;y^{2}$$<br>\r\nHence, the coefficient of the product of $$5x^{2},\\\\; 4y$$ and 2y is 40.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"20\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$5x^{2} \\\\times 4y \\\\times 2y = (5 \\\\times 4 \\\\times 2)(x^{2} \\\\times y \\\\times y) = 40x^{2}\\\\;y^{2}$$<br>\r\nHence, the coefficient of the product of $$5x^{2},\\\\; 4y$$ and 2y is 40.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"50\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$5x^{2} \\\\times 4y \\\\times 2y = (5 \\\\times 4 \\\\times 2)(x^{2} \\\\times y \\\\times y) = 40x^{2}\\\\;y^{2}$$<br>\r\nHence, the coefficient of the product of $$5x^{2},\\\\; 4y$$ and 2y is 40.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"80\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$5x^{2} \\\\times 4y \\\\times 2y = (5 \\\\times 4 \\\\times 2)(x^{2} \\\\times y \\\\times y) = 40x^{2}\\\\;y^{2}$$<br>\r\nHence, the coefficient of the product of $$5x^{2},\\\\; 4y$$ and 2y is 40.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"40\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$5x^{2} \\\\times 4y \\\\times 2y = (5 \\\\times 4 \\\\times 2)(x^{2} \\\\times y \\\\times y) = 40x^{2}\\\\;y^{2}$$<br>\r\nHence, the coefficient of the product of $$5x^{2},\\\\; 4y$$ and 2y is 40.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$5x^{2} \\\\times 4y \\\\times 2y = (5 \\\\times 4 \\\\times 2)(x^{2} \\\\times y \\\\times y) = 40x^{2}\\\\;y^{2}$$<br>\r\nHence, the coefficient of the product of $$5x^{2},\\\\; 4y$$ and 2y is 40.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the product of $$(2x \\\\;\u2013\\\\; 1)(3x + 4)$$?\",\n                    \"text\": \"What is the product of $$(2x \\\\;\u2013\\\\; 1)(3x + 4)$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$(2x \\\\;\u2013\\\\; 1)(3x + 4)$$<br>\r\n$$= 6x^{2} + 8x \\\\;\u2013\\\\; 3x \\\\;\u2013\\\\; 4$$<br>\r\n$$= 6x^{2} + 5x \\\\;\u2013\\\\; 4$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$6x^{2} + 8x \\\\;\u2013\\\\; 1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(2x \\\\;\u2013\\\\; 1)(3x + 4)$$<br>\r\n$$= 6x^{2} + 8x \\\\;\u2013\\\\; 3x \\\\;\u2013\\\\; 4$$<br>\r\n$$= 6x^{2} + 5x \\\\;\u2013\\\\; 4$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$6x^{2} + 2x \\\\;\u2013\\\\; 4$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(2x \\\\;\u2013\\\\; 1)(3x + 4)$$<br>\r\n$$= 6x^{2} + 8x \\\\;\u2013\\\\; 3x \\\\;\u2013\\\\; 4$$<br>\r\n$$= 6x^{2} + 5x \\\\;\u2013\\\\; 4$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$6x^{2} + x \\\\;\u2013\\\\; 4$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(2x \\\\;\u2013\\\\; 1)(3x + 4)$$<br>\r\n$$= 6x^{2} + 8x \\\\;\u2013\\\\; 3x \\\\;\u2013\\\\; 4$$<br>\r\n$$= 6x^{2} + 5x \\\\;\u2013\\\\; 4$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$6x^{2} + 5x \\\\;\u2013\\\\; 4$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$(2x \\\\;\u2013\\\\; 1)(3x + 4)$$<br>\r\n$$= 6x^{2} + 8x \\\\;\u2013\\\\; 3x \\\\;\u2013\\\\; 4$$<br>\r\n$$= 6x^{2} + 5x \\\\;\u2013\\\\; 4$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$(2x \\\\;\u2013\\\\; 1)(3x + 4)$$<br>\r\n$$= 6x^{2} + 8x \\\\;\u2013\\\\; 3x \\\\;\u2013\\\\; 4$$<br>\r\n$$= 6x^{2} + 5x \\\\;\u2013\\\\; 4$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The product of $$(l + 3m)$$ and $$(l\\\\;-\\\\;2m)$$ is equal to:\",\n                    \"text\": \"The product of $$(l + 3m)$$ and $$(l\\\\;-\\\\;2m)$$ is equal to:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Required product $$= (l + 3m) (l \\\\;-\\\\; 2m)$$<br>\r\n                 $$= l^{2} \\\\;-\\\\; 2ml + 3ml \\\\;-\\\\; 6m^{2}$$<br>\r\n                 $$= l^{2} + ml \\\\;-\\\\; 6m^{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$l^{2} + 3ml + 8m^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Required product $$= (l + 3m) (l \\\\;-\\\\; 2m)$$<br>\r\n                 $$= l^{2} \\\\;-\\\\; 2ml + 3ml \\\\;-\\\\; 6m^{2}$$<br>\r\n                 $$= l^{2} + ml \\\\;-\\\\; 6m^{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2l^{2} \\\\;-\\\\; ml \\\\;-\\\\; m^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Required product $$= (l + 3m) (l \\\\;-\\\\; 2m)$$<br>\r\n                 $$= l^{2} \\\\;-\\\\; 2ml + 3ml \\\\;-\\\\; 6m^{2}$$<br>\r\n                 $$= l^{2} + ml \\\\;-\\\\; 6m^{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$l^{2} + 5ml + 5m^{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Required product $$= (l + 3m) (l \\\\;-\\\\; 2m)$$<br>\r\n                 $$= l^{2} \\\\;-\\\\; 2ml + 3ml \\\\;-\\\\; 6m^{2}$$<br>\r\n                 $$= l^{2} + ml \\\\;-\\\\; 6m^{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$l^{2} + ml \\\\;-\\\\; 6m^{2}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Required product $$= (l + 3m) (l \\\\;-\\\\; 2m)$$<br>\r\n                 $$= l^{2} \\\\;-\\\\; 2ml + 3ml \\\\;-\\\\; 6m^{2}$$<br>\r\n                 $$= l^{2} + ml \\\\;-\\\\; 6m^{2}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Required product $$= (l + 3m) (l \\\\;-\\\\; 2m)$$<br>\r\n                 $$= l^{2} \\\\;-\\\\; 2ml + 3ml \\\\;-\\\\; 6m^{2}$$<br>\r\n                 $$= l^{2} + ml \\\\;-\\\\; 6m^{2}$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"14-frequently-asked-questions-on-multiplying-polynomials\">Frequently Asked Questions on Multiplying Polynomials<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-f13e878c-7b71-4806-a44f-111cd14613ec\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-f13e878c-7b71-4806-a44f-111cd14613ec\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f13e878c-7b71-4806-a44f-111cd14613ec\"><strong>What is binomial?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-f13e878c-7b71-4806-a44f-111cd14613ec\">\n\n<p>A polynomial that has only two terms is called a binomial.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-f13e878c-7b71-4806-a44f-111cd14613ec\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f13e878c-7b71-4806-a44f-111cd14613ec\"><strong>What is trinomial?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-f13e878c-7b71-4806-a44f-111cd14613ec\">\n\n<p>A polynomial that has only three terms is called a trinomial.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-f13e878c-7b71-4806-a44f-111cd14613ec\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f13e878c-7b71-4806-a44f-111cd14613ec\"><strong>How do you multiply polynomials with mixed variables?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-f13e878c-7b71-4806-a44f-111cd14613ec\">\n\n<p>Multiply all the coefficients. Multiply the same variables using the laws of exponents. Multiply these two products with the remaining variables to get the answer.Example: $5x \\times 2xy \\times 5xyz = 50x^{3}\\;y^{2}\\;z$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-f13e878c-7b71-4806-a44f-111cd14613ec\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f13e878c-7b71-4806-a44f-111cd14613ec\"><strong>What is the product of two or more monomials?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-f13e878c-7b71-4806-a44f-111cd14613ec\">\n\n<p>The product of two or more monomials is also a monomial.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-f13e878c-7b71-4806-a44f-111cd14613ec\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f13e878c-7b71-4806-a44f-111cd14613ec\"><strong>What is the degree of the product polynomial when multiplying two polynomials of the same degree?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-f13e878c-7b71-4806-a44f-111cd14613ec\">\n\n<p>When multiplying two polynomials of the same degree, the degree of the product polynomial is twice the degree of the two polynomials being multiplied.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Multiplication of Polynomials? To multiply two polynomials, we use the distributive property of multiplication where we multiply each term of the first polynomial by each term of the second polynomial. While doing so, we multiply variables with variables, coefficients with coefficients, and finally add all the results together. There are different types &#8230; <a title=\"Multiplying Polynomials: Definition, Steps, Methods, Examples, Facts\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplying-polynomials\" aria-label=\"More on Multiplying Polynomials: Definition, Steps, Methods, Examples, Facts\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-31750","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31750","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=31750"}],"version-history":[{"count":12,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31750\/revisions"}],"predecessor-version":[{"id":31768,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31750\/revisions\/31768"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=31750"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=31750"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=31750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}