{"id":31846,"date":"2023-07-13T16:25:10","date_gmt":"2023-07-13T16:25:10","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=31846"},"modified":"2023-07-16T03:43:04","modified_gmt":"2023-07-16T03:43:04","slug":"subtracting-polynomials-definition-methods-examples-steps-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/subtracting-polynomials","title":{"rendered":"Subtracting Polynomials: Definition, Methods, Examples, Steps, FAQs"},"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-01972917-c3cf-4d99-aa66-cce5c4783bb8\" 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\/subtracting-polynomials#0-what-is-subtracting-polynomials>What Is Subtracting Polynomials?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/subtracting-polynomials#2-horizontal-method-of-subtracting-polynomials>Horizontal Method of Subtracting Polynomials<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/subtracting-polynomials#3-vertical-method-of-subtracting-polynomials>Vertical Method of Subtracting Polynomials<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/subtracting-polynomials#6-solved-examples-of-subtracting-polynomials>Solved Examples of Subtracting Polynomials<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/subtracting-polynomials#7-practice-problems-on-subtracting-polynomials>Practice Problems on Subtracting Polynomials<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/subtracting-polynomials#8-frequently-asked-questions-about-subtracting-polynomials>Frequently Asked Questions about Subtracting Polynomials<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-subtracting-polynomials\">What Is Subtracting Polynomials?<\/h2>\n\n\n\n<p>Subtracting polynomials follows a similar procedure as adding polynomials. We just have to deal with the minus sign $(\\;-\\;)$ in between.<\/p>\n\n\n\n<p>Consider the expression p$(x)\\;-\\;q(x)$ representing the subtraction of polynomials. Here, we are subtracting q(x) from p(x). Due to the minus sign before q(x), the signs of all the terms in the polynomial q(x) are changed (\u201c$+$ changes to $-$\u201d and \u201c$-$ changes to $+$\u201d). Next, we simplify by combining the like terms and find the answer.<\/p>\n\n\n\n<p>In simple words, when subtracting polynomials, we reverse the signs of each <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/term\">term<\/a> in the second polynomial and then add the polynomials as usual.<\/p>\n\n\n\n<p>Let us see how to <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/subtraction\/subtract\">subtract<\/a> polynomials.<\/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\/find-the-difference-by-subtracting-multiples-of-10\" 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\/add_sub_pv_sub_2d_1d_horizontal_pt.png\" alt=\"Find the Difference by Subtracting Multiples of 10 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 Difference by Subtracting Multiples of 10 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\/match-by-subtracting-from-a-teen-number\" 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\/add_sub_facts_sub_from_teen_no_1_pt.png\" alt=\"Match by Subtracting from a Teen Number 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\">Match by Subtracting from a Teen Number 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\/measure-lengths-in-half-inches-by-subtracting\" 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_length_half_inches_sub_pt.png\" alt=\"Measure Lengths in Half-inches by Subtracting 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\">Measure Lengths in Half-inches by Subtracting 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\/measure-lengths-in-inches-by-subtracting\" 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_length_inches_sub_pt.png\" alt=\"Measure Lengths in Inches by Subtracting 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\">Measure Lengths in Inches by Subtracting 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\/measure-lengths-on-a-ruler-by-subtracting\" 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_length_ruler_sub_pt.png\" alt=\"Measure Lengths on a Ruler by Subtracting 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\">Measure Lengths on a Ruler by Subtracting 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\/solve-by-subtracting-multiples-of-100\" 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\/add_sub_pv_sub_hundreds_match_pt.png\" alt=\"Solve by Subtracting Multiples of 100 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\">Solve by Subtracting Multiples of 100 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\/solve-word-problems-on-subtracting-money\" 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\/money_money_sub_wp_2_pt.png\" alt=\"Solve Word Problems on Subtracting Money 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\">Solve Word Problems on Subtracting Money 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\/subtracting-1-digit-number-from-3-digit-number\" 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\/add_sub_pv_sub_3d_1d_horizontal_pt.png\" alt=\"Subtracting 1-Digit Number from 3-Digit Number 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\">Subtracting 1-Digit Number from 3-Digit Number 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\/subtracting-10-from-3-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\/add_sub_pv_sub_10_match_pt.png\" alt=\"Subtracting 10 from 3-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\">Subtracting 10 from 3-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\/subtracting-10-from-teen-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\/add_sub_facts_sub_10_g2_pt.png\" alt=\"Subtracting 10 from Teen 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\">Subtracting 10 from Teen 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><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-methods-of-subtracting-polynomials\">Methods of Subtracting Polynomials<\/h2>\n\n\n\n<p>There are two ways to subtract polynomials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Subtracting polynomials horizontally<\/li>\n\n\n\n<li>Subtracting polynomials vertically<\/li>\n<\/ul>\n\n\n\n<p>Regardless of which<strong> method of subtracting polynomials we use<\/strong>, the idea and the procedure is the same. The only difference is the arrangement or placement of polynomials during the subtraction operation.&nbsp;<\/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\/real-life-problems-on-subtracting-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\/real-life-problems-on-subtracting-fractions.jpeg\" alt=\"Real Life Problems on Subtracting 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\/real-life-problems-on-subtracting-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\/real-life-problems-on-subtracting-mixed-numbers.jpeg\" alt=\"Real Life Problems on Subtracting 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\/story-problems-on-subtracting-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\/story-problems-on-subtracting-fractions.jpeg\" alt=\"Story Problems on Subtracting 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\/subtracting-1-digit-numbers-from-3-digit-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\/subtracting-1-digit-numbers-from-3-digit-numbers.jpeg\" alt=\"Subtracting 1-Digit Numbers from 3-Digit 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\/subtracting-10-from-3-digit-numbers-horizontal-subtraction\" 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\/subtracting-10-from-3-digit-numbers-horizontal-subtraction.jpeg\" alt=\"Subtracting 10 from 3-Digit Numbers: Horizontal Subtraction 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\/subtracting-10-from-3-digit-numbers-horizontal-timed-practice\" 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\/subtracting-10-from-3-digit-numbers-horizontal-timed-practice.jpeg\" alt=\"Subtracting 10 from 3-Digit Numbers: Horizontal Timed Practice\">\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\/subtracting-10-from-3-digit-numbers-vertical-subtraction\" 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\/subtracting-10-from-3-digit-numbers-vertical-subtraction.jpeg\" alt=\"Subtracting 10 from 3-Digit Numbers: Vertical Subtraction 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\/subtracting-10-from-3-digit-numbers-vertical-timed-practice\" 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\/subtracting-10-from-3-digit-numbers-vertical-timed-practice.jpeg\" alt=\"Subtracting 10 from 3-Digit Numbers: Vertical Timed Practice\">\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\/subtracting-2-digit-numbers-from-3-digit-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\/subtracting-2-digit-numbers-from-3-digit-numbers.jpeg\" alt=\"Subtracting 2-Digit Numbers from 3-Digit 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\/subtracting-fractions-using-visual-model\" 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\/subtracting-fractions-using-visual-model.jpeg\" alt=\"Subtracting Fractions Using Visual Model 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-horizontal-method-of-subtracting-polynomials\">Horizontal Method of Subtracting Polynomials<\/h2>\n\n\n\n<p>Take a look at the steps required for the horizontal method of<strong> subtracting polynomials <\/strong>with an example.<\/p>\n\n\n\n<p><strong>Example: Subtract <\/strong>$P = 2x^{3} \\;-\\; 3y^{2} + 3z$ from $Q = 7y^{2} + 5x^{3} \\;\u2013\\; 2z$<strong>.<\/strong><\/p>\n\n\n\n<p>Here,&nbsp; $P = 2x^{3} \\;-\\; 3y^{2} + 3z$ and $Q = 7y^{2} + 5x^{3} \\;\u2013\\; 2z$<\/p>\n\n\n\n<p>We have to find Q &#8211; P.<\/p>\n\n\n\n<p><strong>Step 1: <\/strong>Arrange the two polynomials in the standard forms.<\/p>\n\n\n\n<p>$Q = 7y^{2} + 5x^{3} \\;\u2013\\; 2z = 5x^{3} + 7y^{2} \\;-\\; 2z$<\/p>\n\n\n\n<p>$P = 2x^{3} \\;-\\; 3y^{2} + 3z$<strong> <\/strong>is already in the standard form.<\/p>\n\n\n\n<p><strong>Step 2: <\/strong>Place them horizontally separated by minus sign (\u2013) such that the second polynomial is in the parentheses.<\/p>\n\n\n\n<p>$Q \\;-\\; P = (5x^{3} + 7y^{2} \\;-\\; 2z) \\;\u2013\\; (2x^{3} \\;-\\; 3y^{2} + 3z)$<\/p>\n\n\n\n<p><strong>Step 3: <\/strong>Remove the parentheses. For the second polynomial, change the sign of each term after removing the parentheses.&nbsp;<\/p>\n\n\n\n<p>$Q \\;-\\; P = 5x^{3} + 7y^{2} \\;-\\; 2z \\;\u2013\\; (2x^{3} \\;-\\; 3y^{2} + 3z)$<\/p>\n\n\n\n<p>$Q \\;-\\; P = 7y^{2} + 5x^{3} \\;\u2013\\; 2z \\;\u2013\\; 2x^{3} + 3y^{2} \\;-\\; 3z$<\/p>\n\n\n\n<p><strong>Step 4: <\/strong>Arrange all like terms together and solve.<\/p>\n\n\n\n<p>$Q \\;-\\; P = 5x^{3} \\;-\\; 2x^{3} + 7y^{2} + 3y^{2} \\;-\\; 2z \\;-\\;3z$<\/p>\n\n\n\n<p>$Q \\;-\\; P = 3x^{3} + 10y^{2} \\;-\\; 5z$&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-vertical-method-of-subtracting-polynomials\">Vertical Method of Subtracting Polynomials<\/h2>\n\n\n\n<p>In the vertical method, all the equations are arranged in columns according to the like terms. The signs are changed and the operation takes place.&nbsp;<\/p>\n\n\n\n<p>Take a look at the example of a vertical <strong>method of subtracting polynomials<\/strong> given below:<\/p>\n\n\n\n<p><strong>Find: <\/strong>$(7x \\;\u2013\\; 3y + 6z) \\;-\\; x \\;\u2013\\; 4y \\;\u2013\\; 2z$<strong> <\/strong>using the vertical method.<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Arrange the two polynomials in the standard form.<\/p>\n\n\n\n<p>Here, both polynomials are already in the standard form.<\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Arrange the expressions one below the other such that the polynomial being subtracted is at the bottom. Align the like terms. There will be two rows, in which the lower row is subtracted from the upper row.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"404\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/subtracting-polynomials-vertically.png\" alt=\"Subtracting polynomials vertically\" class=\"wp-image-31851\" title=\"Subtracting polynomials vertically\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/subtracting-polynomials-vertically.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/subtracting-polynomials-vertically-300x195.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Step 3:<\/strong> Change the signs of all the terms of the second row; positive changes to negative and negative sign changes to positive. Finally, add the like terms.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"404\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/vertical-method-of-subtracting-polynomials-example.png\" alt=\"Vertical method of subtracting polynomials - example\" class=\"wp-image-31852\" title=\"Vertical method of subtracting polynomials - example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/vertical-method-of-subtracting-polynomials-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/vertical-method-of-subtracting-polynomials-example-300x195.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-facts-on-subtracting-polynomials\">Facts on Subtracting 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>Subtracting polynomials is the same as adding the opposite.<br>For example, 3-5 and 3 + (-5) represent the same thing. Similarly,<br>$(7x \\;-\\; 5y) \\;-\\; (3x + 2y)$ and $(7x \\;-\\; 5y) + (\\;-\\; 3x \\;-\\; 2y)$ are the same.<\/li>\n\n\n\n<li>When subtracting polynomials, it is important to distribute the subtraction sign to each term of the polynomial being subtracted. This means changing the sign of each term before combining like terms.<\/li>\n\n\n\n<li>In <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/algebra\">algebra<\/a>, the like terms are terms having the same variable raised to the same power. In other words, their variable part is the same such that the same variables have the same exponent powers.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned to subtract polynomial expressions, different methods to subtract polynomials, facts and examples. Now, let us practice solving problems by subtracting polynomials.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-solved-examples-of-subtracting-polynomials\">Solved Examples of Subtracting Polynomials<\/h2>\n\n\n\n<p><strong>1. Subtract <\/strong>$2x \\;-\\; 5y + 3z$<strong> from <\/strong>$5x + 9y \\;-\\; 2z$<strong>&nbsp; using the horizontal method.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>We have to find $(5x + 9y \\;\u2013\\; 2z) \\;-\\; (2x \\;-\\; 5y + 3z)$.<\/p>\n\n\n\n<p>Remove the parentheses by multiply the negative sign with the terms<\/p>\n\n\n\n<p>$= 5x + 9y \\;-\\; 2z \\;\u2013\\; 2x + 5y \\;-\\; 3z$<\/p>\n\n\n\n<p>&nbsp;Arrange the like terms together.<\/p>\n\n\n\n<p>$= 5x \\;\u2013\\; 2x + 9y + 5y \\;-\\; 2z \\;-\\; 3z$<\/p>\n\n\n\n<p>$= 3x + 14y \\;-\\; 5z$<\/p>\n\n\n\n<p><strong>2. Subtract <\/strong>$4x \\;-\\; 10y +15z$<strong> from <\/strong>$5x + 8y \\;-\\; 20z$<strong> using the horizontal method.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>$(4x \\;-\\; 10y + 15z) \\;-\\; (5x + 8y \\;-\\; 20z)$<\/p>\n\n\n\n<p>Sign change of the second polynomial by removing the parentheses and multiplying<\/p>\n\n\n\n<p>$= 4x \\;-\\; 10y + 15z \\;-\\; 5x \\;-\\; 8y + 20z$<\/p>\n\n\n\n<p>&nbsp;Combine the like terms.<\/p>\n\n\n\n<p>$= 4x \\;-\\; 5x \\;-\\; 10y \\;-\\; 8y + 15z + 20z$<\/p>\n\n\n\n<p>$= \\;-\\; x \\;-\\; 18y + 35z$<\/p>\n\n\n\n<p><strong>3.&nbsp; Subtract <\/strong>$5x \\;\u2013\\; 3y \\;\u2013\\; 4z$<strong> from <\/strong>$7x \\;\u2013\\; 6y + 6z$<strong> using the vertical method.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>We have to find $7x \\;-\\; 6y + 6z \\;-\\; (5x \\;\u2013\\; 3y \\;\u2013\\; 4z)$.<\/p>\n\n\n\n<p>Arrange the expression in two rows with like terms in the same column. Change the sign of each term of the second row and proceed with the operation.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"276\" height=\"149\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/subtracting-polynomials-vertically-example.png\" alt=\"Subtracting polynomials vertically- example\" class=\"wp-image-31853\" title=\"Subtracting polynomials vertically- example\"\/><\/figure>\n\n\n\n<p><strong>4. Subtract <\/strong>$3a^{3} + 5a^{2} \\;\u2013\\; 7a + 10$<strong> from <\/strong>$6a^{3} \\;-\\; 8a^{2} + a + 10$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>$6a^{3} \\;-\\; 8a^{2} + a + 10 \\;-\\;(3a^{3} + 5a^{2} \\;\u2013\\; 7a + 10)$<\/p>\n\n\n\n<p>Arrange the expression in two rows with like terms in the same column. Change the sign of each term of the second row and proceed with the operation.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"279\" height=\"137\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/example-on-subtracting-polynomials-vertically.png\" alt=\"Example on subtracting polynomials vertically\" class=\"wp-image-31854\" title=\"Example on subtracting polynomials vertically\"\/><\/figure>\n\n\n\n<p>Thus,&nbsp;<\/p>\n\n\n\n<p>$6a^{3} \\;-\\; 8a^{2} + a + 10 \\;-\\; (3a^{3} + 5a^{2} \\;\u2013\\; 7a + 10)$<\/p>\n\n\n\n<p>$= 3a^{3} \\;-\\; 13a^{2} + 8a \\;-\\; 0$<br><\/p>\n\n\n\n<p><strong>5. Subtract the polynomials horizontally <\/strong>$15x^{3} + 12y^{2} \\;-\\; 8z \\;-\\; 7$ <strong>from <\/strong>$20x^{3} \\;-\\; 6y^{2} + 31z + 9$.<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>We have to find $20x^{3} \\;-\\; 6y^{2} + 31z + 9 \\;-\\; (15x^{3} + 12y^{2} \\;-\\; 8z \\;-\\; 7)$.<\/p>\n\n\n\n<p>&nbsp;Sign change of the second polynomial through the parentheses<\/p>\n\n\n\n<p>$= 20x^{3} \\;-\\; 6y^{2} + 31z + 9 \\;-\\; 15x^{3} \\;-\\; 12y^{2} + 8z + 7$<\/p>\n\n\n\n<p>&nbsp;Combine the like terms.<\/p>\n\n\n\n<p>$= 20x^{3} \\;-\\; 15x^{3} \\;-\\; 6y^{2} \\;-\\; 12y^{2} + 31z + 8z + 9 + 7$<\/p>\n\n\n\n<p>$= 5x^{3} \\;-\\; 18y^{2} + 39z +16$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-practice-problems-on-subtracting-polynomials\">Practice Problems on Subtracting Polynomials<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Subtracting Polynomials: Definition, Methods, Examples, Steps, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Solve: $(5x\\;-\\;2y + 1)\\;-\\;(2x\\;-\\;7y + 4)$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$3x + 5y\\;-\\;3$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$7x + 5y + 5$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$3x\\;-\\;5y\\;-\\;3$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$3x\\;-\\;9y + 3$<\/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: $3x + 5y\\;-\\;3$<br\/>$(5x\\;-\\;2y + 1)\\;-\\;(2x\\;-\\;7y + 4)$<br>\r\n$=  3x + 5y\\;-\\;3$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">$(12p^{2} + 15p + 3)\\;-\\;(2p^{2} + 17p\\;-\\;2) =$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$10p^{2} + 2p\\;-\\;5$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$10p^{2}\\;-\\;2p + 5$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$10p^{2} + 2p\\;-\\;1$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$10p^{2}\\;-\\;2p + 1$<\/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: $10p^{2}\\;-\\;2p + 5$<br\/>$(12p^{2} + 15p + 3)\\;-\\;(2p^{2} + 17p\\;-\\;2)$<br>\r\n$= 10p^{2}\\;-\\;2p + 5$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">$(x + y)\\;-\\;(y\\;-\\;x)=$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$2x$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$2y$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$2x + 2y$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$2x\\;-\\; 2y$<\/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: $2x$<br\/>$(x + y)\\;-\\;(y\\;-\\;x) = x + y\\;-\\;y + x = 2x$<\/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     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5y\\\\;-\\\\;3$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$7x + 5y + 5$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(5x\\\\;-\\\\;2y + 1)\\\\;-\\\\;(2x\\\\;-\\\\;7y + 4)$$<br>\r\n$$=  3x + 5y\\\\;-\\\\;3$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$3x\\\\;-\\\\;5y\\\\;-\\\\;3$$\",\n                               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0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$3x + 5y\\\\;-\\\\;3$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$(5x\\\\;-\\\\;2y + 1)\\\\;-\\\\;(2x\\\\;-\\\\;7y + 4)$$<br>\r\n$$=  3x + 5y\\\\;-\\\\;3$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$(5x\\\\;-\\\\;2y + 1)\\\\;-\\\\;(2x\\\\;-\\\\;7y + 4)$$<br>\r\n$$=  3x + 5y\\\\;-\\\\;3$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"$$(12p^{2} + 15p + 3)\\\\;-\\\\;(2p^{2} + 17p\\\\;-\\\\;2) =$$\",\n                    \"text\": \"$$(12p^{2} + 15p + 3)\\\\;-\\\\;(2p^{2} + 17p\\\\;-\\\\;2) =$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$(12p^{2} + 15p + 3)\\\\;-\\\\;(2p^{2} + 17p\\\\;-\\\\;2)$$<br>\r\n$$= 10p^{2}\\\\;-\\\\;2p + 5$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$10p^{2} + 2p\\\\;-\\\\;5$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(12p^{2} + 15p + 3)\\\\;-\\\\;(2p^{2} + 17p\\\\;-\\\\;2)$$<br>\r\n$$= 10p^{2}\\\\;-\\\\;2p + 5$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$10p^{2} + 2p\\\\;-\\\\;1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(12p^{2} + 15p + 3)\\\\;-\\\\;(2p^{2} + 17p\\\\;-\\\\;2)$$<br>\r\n$$= 10p^{2}\\\\;-\\\\;2p + 5$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$10p^{2}\\\\;-\\\\;2p + 1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(12p^{2} + 15p + 3)\\\\;-\\\\;(2p^{2} + 17p\\\\;-\\\\;2)$$<br>\r\n$$= 10p^{2}\\\\;-\\\\;2p + 5$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$10p^{2}\\\\;-\\\\;2p + 5$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$(12p^{2} + 15p + 3)\\\\;-\\\\;(2p^{2} + 17p\\\\;-\\\\;2)$$<br>\r\n$$= 10p^{2}\\\\;-\\\\;2p + 5$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$(12p^{2} + 15p + 3)\\\\;-\\\\;(2p^{2} + 17p\\\\;-\\\\;2)$$<br>\r\n$$= 10p^{2}\\\\;-\\\\;2p + 5$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"$$(x + y)\\\\;-\\\\;(y\\\\;-\\\\;x)=$$\",\n                    \"text\": \"$$(x + y)\\\\;-\\\\;(y\\\\;-\\\\;x)=$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$(x + y)\\\\;-\\\\;(y\\\\;-\\\\;x) = x + y\\\\;-\\\\;y + x = 2x$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2y$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(x + y)\\\\;-\\\\;(y\\\\;-\\\\;x) = x + y\\\\;-\\\\;y + x = 2x$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2x + 2y$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(x + y)\\\\;-\\\\;(y\\\\;-\\\\;x) = x + y\\\\;-\\\\;y + x = 2x$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2x\\\\;-\\\\; 2y$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$(x + y)\\\\;-\\\\;(y\\\\;-\\\\;x) = x + y\\\\;-\\\\;y + x = 2x$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$2x$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$(x + y)\\\\;-\\\\;(y\\\\;-\\\\;x) = x + y\\\\;-\\\\;y + x = 2x$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$(x + y)\\\\;-\\\\;(y\\\\;-\\\\;x) = x + y\\\\;-\\\\;y + x = 2x$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-frequently-asked-questions-about-subtracting-polynomials\">Frequently Asked Questions about Subtracting Polynomials<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-ac59fa11-3388-4f3e-a6fc-9bc6042a140a\" 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-ac59fa11-3388-4f3e-a6fc-9bc6042a140a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ac59fa11-3388-4f3e-a6fc-9bc6042a140a\"><strong>What property is used when subtracting polynomials?<\/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-ac59fa11-3388-4f3e-a6fc-9bc6042a140a\">\n\n<p>In the procedure of <strong>subtracting polynomials<\/strong>, the distributive property is used. This is also used while adding polynomials.<\/p>\n\n\n\n<p>Example: $(3x^{2} + 2x + 6) + (x^{2} \\;-\\; 6x \\;-\\; 10)$<\/p>\n\n\n\n<p>$= (3 + 1)x^{2} + (2 \\;-\\; 6)x + (6 \\;-\\; 10)$<\/p>\n\n\n\n<p>$= 4x^{2} \\;-\\; 4x \\;-\\; 4$<\/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-ac59fa11-3388-4f3e-a6fc-9bc6042a140a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ac59fa11-3388-4f3e-a6fc-9bc6042a140a\"><strong>What is the rule followed while subtracting polynomials?<\/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-ac59fa11-3388-4f3e-a6fc-9bc6042a140a\">\n\n<p>There are two important rules to follow while subtracting polynomials. They are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Arrange the like terms together while performing subtraction.<\/li>\n<\/ul>\n\n\n\n<p>Signs of each term of the subtracting polynomial should be changed. That is \u201c$+$\u201d changes to \u201c$-$\u201d and \u201c$-$\u201d changes to \u201c$+$.\u201d<\/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-ac59fa11-3388-4f3e-a6fc-9bc6042a140a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-ac59fa11-3388-4f3e-a6fc-9bc6042a140a\"><strong>How can subtracting polynomials be simplified?<\/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-ac59fa11-3388-4f3e-a6fc-9bc6042a140a\">\n\n<p>Subtracting polynomials can be simplified by converting the problem from subtraction to addition. Change all the signs of the terms of the second polynomials through the parentheses, that is \u201c$+$\u201d changes to \u201c$-$\u201d and \u201c-\u201d changes to \u201c$+$.\u201d Once it is done, the normal addition of polynomials is performed.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Subtracting Polynomials? Subtracting polynomials follows a similar procedure as adding polynomials. We just have to deal with the minus sign $(\\;-\\;)$ in between. Consider the expression p$(x)\\;-\\;q(x)$ representing the subtraction of polynomials. Here, we are subtracting q(x) from p(x). Due to the minus sign before q(x), the signs of all the terms in &#8230; <a title=\"Subtracting Polynomials: Definition, Methods, Examples, Steps, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/subtracting-polynomials\" aria-label=\"More on Subtracting Polynomials: Definition, Methods, Examples, Steps, FAQs\">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-31846","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\/31846","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=31846"}],"version-history":[{"count":12,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31846\/revisions"}],"predecessor-version":[{"id":31886,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31846\/revisions\/31886"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=31846"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=31846"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=31846"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}