{"id":34643,"date":"2023-09-25T17:05:00","date_gmt":"2023-09-25T17:05:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=34643"},"modified":"2023-10-04T17:54:03","modified_gmt":"2023-10-04T17:54:03","slug":"ab3-formula-solved-examples-faqs-practice-problems","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/a-plus-b-cube-formula","title":{"rendered":"$(A+B)^{3}$ Formula &#8211; Solved Examples, FAQS, Practice Problems"},"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-704f3cec-581d-41af-9385-465214766a2d\" 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\/a-plus-b-cube-formula#0-what-is-the-a-b-3-formula>What Is the (a + b)3 Formula?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/a-plus-b-cube-formula#2-derivation-of-ab-3-formula>Derivation of (a+b)3 Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/a-plus-b-cube-formula#3-how-to-use-the-ab-3-formula>How to Use the (a+b)3 Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/a-plus-b-cube-formula#6-solved-examples-on-the-ab-3-formula>Solved Examples on the (a+b)3 Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/a-plus-b-cube-formula#7-practice-problems-on-the-a-b-3-formula>Practice Problems on the (a + b)3 Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/a-plus-b-cube-formula#8-frequently-asked-questions-about-the-a-b-3-formula>Frequently Asked Questions about the (a + b)3 Formula<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-a-b-3-formula\">What Is the (a + b)<sup>3<\/sup> Formula?<\/h2>\n\n\n\n<p><strong>In algebra, the (a + b)<sup>3<\/sup> formula allows us to find the cube of a binomial and helps us to simplify <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/expression\"><strong>expressions<\/strong><\/a><strong>.\u00a0<\/strong><\/p>\n\n\n\n<p>The formula for the cube of the sum of two terms, <strong>(a + b)<strong><sup>3<\/sup><\/strong><\/strong>, can be expanded using the binomial theorem or by applying the distributive property multiple times. The result is:<\/p>\n\n\n\n<p>(a + b)<strong><sup>3<\/sup><\/strong> = a<strong><sup>3<\/sup><\/strong> + 3a<sup>2<\/sup>b + 3 ab<strong><sup>2<\/sup><\/strong> + b<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>This formula shows how to find the cube of the sum of a and b by raising both terms to the power of 3, along with the combinations involving a and b raised to the power of 2 and 1.<\/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\/10-and-100-more-than-the-same-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_1_10_100_more_same_num_pt.png\" alt=\"10 and 100 More than the Same 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\">10 and 100 More than the Same 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\/add-1-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_facts_add_make_10_pt.png\" alt=\"Add 1-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\">Add 1-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\/add-10-to-a-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_add_10_number_pt.png\" alt=\"Add 10 to a 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\">Add 10 to a 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\/add-100-to-a-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_add_100_horizontal_pt.png\" alt=\"Add 100 to a 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\">Add 100 to a 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\/add-2-digit-and-1-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_add_2d_1d_match_pt.png\" alt=\"Add 2-Digit and 1-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\">Add 2-Digit and 1-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\/add-2-digit-numbers-by-regrouping\" 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_add_regrp_2d_2d_vertical_pt.png\" alt=\"Add 2-Digit Numbers By Regrouping 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\">Add 2-Digit Numbers By Regrouping 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\/add-3-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_add_3_no_pt.png\" alt=\"Add 3 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\">Add 3 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\/add-3-numbers-in-any-order\" 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_shifty_bridges_4_gm.png\" alt=\"Add 3 Numbers in Any Order 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\">Add 3 Numbers in Any Order 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\/add-3-numbers-using-groups-of-objects\" 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_add_using_model_pt.png\" alt=\"Add 3 Numbers Using Groups of Objects 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\">Add 3 Numbers Using Groups of Objects 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\/add-3-numbers-using-model\" 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_add_3_no_using_models_pt.png\" alt=\"Add 3 Numbers using Model 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\">Add 3 Numbers using Model 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-a-b-3-formula\">(a + b)<strong><sup>3<\/sup><\/strong> Formula<\/h2>\n\n\n\n<p>The (a + b) whole cube formula or (a + b)<strong><sup>3<\/sup><\/strong> formula represents the cube of a binomial. It represents the result of cubing the sum of &#8216;a&#8217; and &#8216;b&#8217;.<\/p>\n\n\n\n<p>(a + b)<strong><sup>3<\/sup><\/strong> = a<strong><sup>3<\/sup><\/strong> + 3a<strong><sup>2<\/sup><\/strong>b + 3ab<strong><sup>2<\/sup> <\/strong>+ b<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>It&#8217;s important to note that this formula holds true for any values assigned to both &#8216;a&#8217; and &#8216;b.&#8217;<\/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\/10-and-100-more-than-a-3-digit-number\" 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\/10-and-100-more-than-a-3-digit-number.jpeg\" alt=\"10 and 100 More than a 3-digit Number\">\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\/100-more-and-100-less-than-a-3-digit-number\" 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\/100-more-and-100-less-than-a-3-digit-number.jpeg\" alt=\"100 More and 100 Less than a 3-digit Number\">\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\/100-more-than-a-3-digit-number\" 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\/100-more-than-a-3-digit-number.jpeg\" alt=\"100 More than a 3-digit Number\">\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\/above-and-below\" 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\/above-and-below.jpeg\" alt=\"Above and Below 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\/add-subtract-multiples-of-10\" 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\/add-subtract-multiples-of-10.jpeg\" alt=\"Add & Subtract Multiples of 10 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\/add-subtract-ones-2-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\/add-subtract-ones-2-digit-numbers.jpeg\" alt=\"Add & Subtract Ones & 2-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\/add-1-digit-and-3-digit-numbers-and-find-the-sum\" 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\/add-1-digit-and-3-digit-numbers-and-find-the-sum.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers and Find the Sum\">\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\/add-1-digit-and-3-digit-numbers-and-match-the-sum\" 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\/add-1-digit-and-3-digit-numbers-and-match-the-sum.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers and Match the Sum\">\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\/add-1-digit-and-3-digit-numbers-using-addition-tables\" 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\/add-1-digit-and-3-digit-numbers-using-addition-tables.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers Using Addition Tables\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" 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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-derivation-of-ab-3-formula\">Derivation of (a+b)<strong><sup>3<\/sup><\/strong> Formula<\/h2>\n\n\n\n<p>To understand the derivation of the a + b whole cube formula, let&#8217;s start by expanding the expression (a + b)<strong><sup>3<\/sup><\/strong>.\u00a0<\/p>\n\n\n\n<p>We can achieve this by multiplying the binomial (a + b) by itself three times:<\/p>\n\n\n\n<p>(a + b)<strong><sup>3<\/sup><\/strong> =\u00a0 (a + b)(a + b)(a + b)\u00a0<\/p>\n\n\n\n<p>On expanding this expression, we get<\/p>\n\n\n\n<p>(a + b)<strong><sup>3<\/sup><\/strong> = (a<strong><sup>2<\/sup><\/strong> + 2ab + b<strong><sup>2<\/sup><\/strong>)(a + b)<\/p>\n\n\n\n<p>Let\u2019s use the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/distributive-property\">distributive property<\/a> to expand the above expression.<\/p>\n\n\n\n<p>(a + b)<strong><sup>3<\/sup><\/strong> = a<strong><sup>3<\/sup><\/strong> + a<strong><sup>2<\/sup><\/strong>b + 2a<strong><sup>2<\/sup><\/strong>b + 2ab<strong><sup>2 <\/sup><\/strong>+ ab<strong><sup>2 <\/sup><\/strong>+ b<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>On combining like terms, we arrive at the final form of the (a + b)<strong><sup>3<\/sup><\/strong> formula:<\/p>\n\n\n\n<p>(a + b)<strong><sup>3<\/sup><\/strong> = a<strong><sup>3<\/sup><\/strong> + 3a<strong><sup>2<\/sup><\/strong>b + 3ab<strong><sup>2<\/sup> <\/strong>+ b<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>Alternatively, we can express the (a + b)<strong><sup>3<\/sup><\/strong> formula as:<\/p>\n\n\n\n<p>(a + b)<strong><sup>3<\/sup><\/strong> = a<strong><sup>3<\/sup><\/strong> + 3ab (a + b) + b<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>This derivation showcases the algebraic manipulation required to arrive at the (a + b)<strong><sup>3<\/sup><\/strong> formula.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-how-to-use-the-ab-3-formula\">How to Use the (a+b)<strong><sup>3<\/sup><\/strong> Formula<\/h2>\n\n\n\n<p>Let\u2019s use the formula (a + b)<strong><sup>3<\/sup><\/strong> = a<strong><sup>3<\/sup><\/strong> + 3a<strong><sup>2<\/sup><\/strong>b + 3ab<strong><sup>2 <\/sup><\/strong>+ b<strong><sup>3<\/sup><\/strong> to expand some expressions.<\/p>\n\n\n\n<p><strong>Example<\/strong>: (x + 2y)<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>Here, a = x, b = 2x<\/p>\n\n\n\n<p>(a + b)<strong><sup>3<\/sup><\/strong> = a<strong><sup>3<\/sup><\/strong> + 3a<strong><sup>2<\/sup><\/strong>b + 3ab<strong><sup>2<\/sup><\/strong> + b<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>(x + 2y)<strong><sup>3<\/sup><\/strong> = x<strong><sup>3<\/sup><\/strong> + 3x<strong><sup>2 <\/sup><\/strong>(2y) + 3x(2y)<strong><sup>2<\/sup><\/strong> + (2y)<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>(x + 2y)<strong><sup>3<\/sup><\/strong> = x<strong><sup>3<\/sup><\/strong> + 6x<strong><sup>2<\/sup><\/strong>y + 3x(4y<strong><sup>2<\/sup><\/strong>) + 8y<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>(x + 2y)<strong><sup>3<\/sup><\/strong> = x<strong><sup>3<\/sup><\/strong> + 6x<strong><sup>2<\/sup><\/strong>y +12xy<strong><sup>2<\/sup><\/strong> + 8y<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-facts-about-the-ab3-formula\">Facts about the (a+b)3 Formula<\/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>The formula (a + b)<strong><sup>3<\/sup><\/strong> represents the cube of the sum of two terms, &#8220;a&#8221; and &#8220;b.&#8221; (a + b)<strong><sup>3<\/sup><\/strong> = a<strong><sup>3<\/sup><\/strong> + 3a<strong><sup>2<\/sup><\/strong>b + 3ab<strong><sup>2<\/sup><\/strong> + b<strong><sup>3<\/sup><\/strong><\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The a plus b whole cube formula represents the cube of the sum of &#8220;a&#8221; and &#8220;b.&#8221; It can also be expressed as (a + b)<strong><sup>3<\/sup><\/strong> = (a + b)$\\times$(a + b)$\\times$(a + b).<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>By the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/commutative-property-of-addition#:~:text=The%20commutative%20property%20of%20addition,will%20give%20the%20same%20answer.\">commutative property of addition<\/a>, we have (a + b)<strong><sup>3<\/sup><\/strong> = (b + a)<strong><sup>3<\/sup><\/strong>.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The (a + b)<strong><sup>3<\/sup><\/strong> formula is part of a group of related formulas known as the binomial coefficients, which are used to expand powers of binomials.\u00a0<\/li>\n<\/ul>\n\n\n\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0For example, (a + b)<strong><sup>2 <\/sup><\/strong>= a<strong><sup>2<\/sup><\/strong> + 2ab + b<strong><sup>2<\/sup><\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The coefficients of the terms in the expansion of (a + b)<strong><sup>3<\/sup><\/strong> correspond to the numbers in the fourth row of Pascal&#8217;s Triangle. Pascal&#8217;s Triangle is a triangular arrangement of numbers where each number is the sum of the two numbers directly above it.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/pascals-triangle.png\" alt=\"Pascals triangle\" class=\"wp-image-34646\" style=\"width:272px;height:337px\" width=\"272\" height=\"337\" title=\"Pascals triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/pascals-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/pascals-triangle-243x300.png 243w\" sizes=\"auto, (max-width: 272px) 100vw, 272px\" \/><\/figure>\n\n\n\n<p><br>In the expansion (a + b)<strong><sup>3<\/sup><\/strong> = a<strong><sup>3<\/sup> <\/strong>+ 3a<strong><sup>2<\/sup><\/strong>b + 3ab<strong><sup>2<\/sup><\/strong> + b<strong><sup>3<\/sup><\/strong>, the coefficients (1, 3, 3, 1) are the same as the fourth row of Pascal&#8217;s Triangle. This relationship between binomial expansions and Pascal&#8217;s Triangle extends to higher powers as well.<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p>The (a+b)3 formula is a powerful tool in algebra for expanding and simplifying cubic binomials. By understanding its derivation, properties, and applications, you can enhance your problem-solving skills and tackle a wide range of mathematical challenges. Let&#8217;s solve some\u00a0 (a + b)<strong><sup>3<\/sup><\/strong> formula examples and practice problems to understand the concept better.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-solved-examples-on-the-ab-3-formula\">Solved Examples on the (a+b)<strong><sup>3<\/sup><\/strong> Formula<\/h2>\n\n\n\n<p><strong>Example 1. Expand (x + 2)<strong><sup>3<\/sup><\/strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Using the (a + b)<strong><sup>3<\/sup><\/strong>\u00a0 formula, we have:<\/p>\n\n\n\n<p>(a + b)<strong><sup>3<\/sup><\/strong> = a<strong><sup>3<\/sup><\/strong> + 3a<strong><sup>2<\/sup><\/strong>b + 3ab<strong><sup>2 <\/sup><\/strong>+ b<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>(x + 2)<strong><sup>3<\/sup><\/strong> = x<strong><sup>3<\/sup><\/strong> + 3x<strong><sup>2<\/sup><\/strong>(2) + 3x(2)<strong><sup>2<\/sup><\/strong> + 2<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>Simplifying each term, we get<\/p>\n\n\n\n<p>(x + 2)<strong><sup>3<\/sup><\/strong> = x<strong><sup>3<\/sup><\/strong> + 6x<strong><sup>2<\/sup><\/strong> + 12x + 8<\/p>\n\n\n\n<p><strong>Example 2: Evaluate 143<sup> <\/sup>using the <\/strong>(a + b)<strong><sup>3<\/sup><\/strong>\u00a0 <strong>formula.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Hare, we can write<strong>&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>14<strong><sup>3<\/sup><\/strong> = (10 + 4)<strong><sup>3<\/sup><\/strong><\/strong><\/p>\n\n\n\n<p>Here, a = 10, b = 4<\/p>\n\n\n\n<p>(a + b)<strong><sup>3<\/sup><\/strong> = a<strong><sup>3<\/sup><\/strong> + 3a<strong><sup>2<\/sup><\/strong>b + 3ab<strong><sup>2<\/sup><\/strong> + b<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p><strong>(10 + 4)<strong><sup>3<\/sup><\/strong> <\/strong>= 10<strong><sup>3<\/sup><\/strong> + 3(10)<strong><sup>2<\/sup><\/strong>(4) + 3(10)(4)<strong><sup>2<\/sup><\/strong> + (4)<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p><strong>(10 + 4)<strong><sup>3<\/sup><\/strong> <\/strong>= 1000 + 3(100)(4) + 3(10)(16) + 64<\/p>\n\n\n\n<p><strong>(10 + 4)<strong><sup>3<\/sup><\/strong> <\/strong>= 1000 + 1200 + 480 + 64<\/p>\n\n\n\n<p><strong>(10 + 4)<strong><sup>3<\/sup><\/strong> <\/strong>= 2744<\/p>\n\n\n\n<p><strong>14<strong><sup>3<\/sup><\/strong><\/strong> <strong>= 2744<\/strong><\/p>\n\n\n\n<p><strong>Example 3: Find the coefficient of the term <\/strong><strong>a\u00b2b<\/strong><strong> in the expansion of <\/strong><strong>(3a + 2b)\u00b3<\/strong><strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Using the (a + b)<strong><sup>3<\/sup><\/strong> formula, we get<\/p>\n\n\n\n<p>(3a + 2b)<strong><sup>3<\/sup><\/strong> = (3a)<strong><sup>3<\/sup><\/strong> + 3(3a)<strong><sup>2<\/sup><\/strong>(2b) + 3(3a)(2b)<strong><sup>2<\/sup><\/strong> + (2b)<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>(3a + 2b)<strong><sup>3<\/sup><\/strong> = 27a<strong><sup>3<\/sup><\/strong> + 3(9a<strong><sup>2<\/sup><\/strong>)2b + 3(3a)(4b<strong><sup>2<\/sup><\/strong>) + 8b<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>(3a + 2b)<strong><sup>3<\/sup><\/strong> = 27a<strong><sup>3<\/sup><\/strong> + 54a<strong><sup>2<\/sup><\/strong>b +36ab<strong><sup>2 <\/sup><\/strong>+ 8b<strong><sup>3<\/sup><\/strong><\/p>\n\n\n\n<p>So, the coefficient of the term involving &#8220;<strong>a\u00b2b<\/strong>&#8221; is 54.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-practice-problems-on-the-a-b-3-formula\">Practice Problems on the (a + b)<strong><sup>3<\/sup><\/strong> Formula<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">$(A+B)^{3}$ Formula - Solved Examples, FAQS, Practice Problems<\/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 expansion of $(a + b)^{3}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$a^{3} + b^{3}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$(a^{2} + 2ab + b^{2})$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$a^{3} + 2a^{2}b + 2ab^{2} + b^{3}$<\/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: $a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$<br\/>The correct expansion of $(a + b)^{3}$ is $a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$.<\/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\">What does $(a + b)^{3}$ represent?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Square of the sum of a and b<\/div><div class=\"spq_answer_block\" data-value=\"1\">Cube of the sum of a and b<\/div><div class=\"spq_answer_block\" data-value=\"2\">Sum of cubes of a and b<\/div><div class=\"spq_answer_block\" data-value=\"3\">Product of a and b raised to the power of 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: Cube of the sum of a and b<br\/>The $(a + b)^{3}$ formula represents the cube of the sum of a and b<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which pattern do the coefficients in the expansion of $(a + b)^{3}$ follow?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Sequential increase<\/div><div class=\"spq_answer_block\" data-value=\"1\">Steady multiplication<\/div><div class=\"spq_answer_block\" data-value=\"2\">Pascal's triangle arrangement<\/div><div class=\"spq_answer_block\" data-value=\"3\">Fibonacci number sequence<\/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: Pascal's triangle arrangement<br\/>The coefficients in the expansion of $(a + b)^{3}$ follow the arrangement of Pascal's triangle, where each coefficient is obtained by adding the two coefficients directly above it.<\/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 expanded form of $(x + 2y)^{3}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$x^{3} + 2y^{3}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$x^{3} + 6x^{2}y + 12xy^{2} + 8y^{3}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$x^{3} + 3x^{2}y + 3xy^{2} + 2y^{3}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$x^{3} + 3xy$<\/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: $x^{3} + 6x^{2}y + 12xy^{2} + 8y^{3}$<br\/>The expansion of $(x + 2y)^{3}$ is obtained by applying the $(a + b)^{3}$ formula, resulting in $x^{3} + 6x^{2}y + 12xy^{2} + 8y^{3}$<\/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\": \"$$(A+B)^{3}$$ Formula - Solved Examples, FAQS, Practice Problems\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"(A+B)^{3} Formula\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the expansion of $$(a + b)^{3}$$?\",\n                    \"text\": \"What is the expansion of $$(a + b)^{3}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The correct expansion of $$(a + b)^{3}$$ is $$a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$a^{3} + b^{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The correct expansion of $$(a + b)^{3}$$ is $$a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(a^{2} + 2ab + b^{2})$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The correct expansion of $$(a + b)^{3}$$ is $$a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$a^{3} + 2a^{2}b + 2ab^{2} + b^{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The correct expansion of $$(a + b)^{3}$$ is $$a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The correct expansion of $$(a + b)^{3}$$ is $$a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The correct expansion of $$(a + b)^{3}$$ is $$a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What does $$(a + b)^{3}$$ represent?\",\n                    \"text\": \"What does $$(a + b)^{3}$$ represent?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The $$(a + b)^{3}$$ formula represents the cube of the sum of a and b\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Square of the sum of a and b\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The $$(a + b)^{3}$$ formula represents the cube of the sum of a and b\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Sum of cubes of a and b\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The $$(a + b)^{3}$$ formula represents the cube of the sum of a and b\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Product of a and b raised to the power of 3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The $$(a + b)^{3}$$ formula represents the cube of the sum of a and b\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Cube of the sum of a and b\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The $$(a + b)^{3}$$ formula represents the cube of the sum of a and b\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The $$(a + b)^{3}$$ formula represents the cube of the sum of a and b\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which pattern do the coefficients in the expansion of $$(a + b)^{3}$$ follow?\",\n                    \"text\": \"Which pattern do the coefficients in the expansion of $$(a + b)^{3}$$ follow?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The coefficients in the expansion of $$(a + b)^{3}$$ follow the arrangement of Pascal's triangle, where each coefficient is obtained by adding the two coefficients directly above it.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Sequential increase\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The coefficients in the expansion of $$(a + b)^{3}$$ follow the arrangement of Pascal's triangle, where each coefficient is obtained by adding the two coefficients directly above it.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Steady multiplication\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The coefficients in the expansion of $$(a + b)^{3}$$ follow the arrangement of Pascal's triangle, where each coefficient is obtained by adding the two coefficients directly above it.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Fibonacci number sequence\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The coefficients in the expansion of $$(a + b)^{3}$$ follow the arrangement of Pascal's triangle, where each coefficient is obtained by adding the two coefficients directly above it.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Pascal's triangle arrangement\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The coefficients in the expansion of $$(a + b)^{3}$$ follow the arrangement of Pascal's triangle, where each coefficient is obtained by adding the two coefficients directly above it.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The coefficients in the expansion of $$(a + b)^{3}$$ follow the arrangement of Pascal's triangle, where each coefficient is obtained by adding the two coefficients directly above it.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the expanded form of $$(x + 2y)^{3}$$?\",\n                    \"text\": \"What is the expanded form of $$(x + 2y)^{3}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The expansion of $$(x + 2y)^{3}$$ is obtained by applying the $$(a + b)^{3}$$ formula, resulting in $$x^{3} + 6x^{2}y + 12xy^{2} + 8y^{3}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x^{3} + 2y^{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The expansion of $$(x + 2y)^{3}$$ is obtained by applying the $$(a + b)^{3}$$ formula, resulting in $$x^{3} + 6x^{2}y + 12xy^{2} + 8y^{3}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x^{3} + 3x^{2}y + 3xy^{2} + 2y^{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The expansion of $$(x + 2y)^{3}$$ is obtained by applying the $$(a + b)^{3}$$ formula, resulting in $$x^{3} + 6x^{2}y + 12xy^{2} + 8y^{3}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x^{3} + 3xy$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The expansion of $$(x + 2y)^{3}$$ is obtained by applying the $$(a + b)^{3}$$ formula, resulting in $$x^{3} + 6x^{2}y + 12xy^{2} + 8y^{3}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$x^{3} + 6x^{2}y + 12xy^{2} + 8y^{3}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The expansion of $$(x + 2y)^{3}$$ is obtained by applying the $$(a + b)^{3}$$ formula, resulting in $$x^{3} + 6x^{2}y + 12xy^{2} + 8y^{3}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The expansion of $$(x + 2y)^{3}$$ is obtained by applying the $$(a + b)^{3}$$ formula, resulting in $$x^{3} + 6x^{2}y + 12xy^{2} + 8y^{3}$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-frequently-asked-questions-about-the-a-b-3-formula\">Frequently Asked Questions about the (a + b)<strong><sup>3<\/sup><\/strong> Formula<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-02e1b355-af95-4db1-9885-20cccdd56a63\" 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-0-02e1b355-af95-4db1-9885-20cccdd56a63\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-02e1b355-af95-4db1-9885-20cccdd56a63\"><strong>What is the purpose of the (a + b)<strong><sup>3<\/sup><\/strong> formula?<\/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-0-02e1b355-af95-4db1-9885-20cccdd56a63\">\n\n<p>The formula is used to expand and simplify cubic binomials, making algebraic manipulations easier.<\/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-1-02e1b355-af95-4db1-9885-20cccdd56a63\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-02e1b355-af95-4db1-9885-20cccdd56a63\"><strong>Can the (a + b)<strong><strong><sup>3<\/sup><\/strong><\/strong> formula be applied to other powers?<\/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-1-02e1b355-af95-4db1-9885-20cccdd56a63\">\n\n<p>Yes, the formula is a specific case of the binomial theorem and can be extended to any positive integer power.<\/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-2-02e1b355-af95-4db1-9885-20cccdd56a63\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-02e1b355-af95-4db1-9885-20cccdd56a63\"><strong>How can the (a + b)<strong><strong><sup>3<\/sup><\/strong><\/strong> formula be proven geometrically?<\/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-2-02e1b355-af95-4db1-9885-20cccdd56a63\">\n\n<p>By visualizing a cube with side lengths (a+b) and observing how its faces, edges, and corners correspond to the expanded terms.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"305\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/visualizing-ab3.png\" alt=\"Visualizing (a+b)3\" class=\"wp-image-34647\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/visualizing-ab3.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/visualizing-ab3-300x148.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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-3-02e1b355-af95-4db1-9885-20cccdd56a63\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-02e1b355-af95-4db1-9885-20cccdd56a63\"><strong>What is the coefficient pattern in the expansion of (a + b)<strong><strong><strong><sup>3<\/sup><\/strong><\/strong><\/strong>?<\/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-3-02e1b355-af95-4db1-9885-20cccdd56a63\">\n\n<p>The coefficients follow Pascal&#8217;s triangle: 1, 3, 3, 1.<\/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-4-02e1b355-af95-4db1-9885-20cccdd56a63\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-02e1b355-af95-4db1-9885-20cccdd56a63\"><strong>How is the (a + b)<strong><strong><strong><strong><sup>3<\/sup><\/strong><\/strong><\/strong><\/strong> formula related to real-world problems?<\/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-4-02e1b355-af95-4db1-9885-20cccdd56a63\">\n\n<p>The (a + b)<strong><strong><strong><strong><strong><sup>3<\/sup><\/strong><\/strong><\/strong><\/strong><\/strong> formula is applicable in various contexts like <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/geometry\">geometry<\/a>, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/algebra\">algebra<\/a>, and physics. It can be used to calculate volumes, areas, perimeters, and other quantities involving dimensions.<\/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-5-02e1b355-af95-4db1-9885-20cccdd56a63\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-02e1b355-af95-4db1-9885-20cccdd56a63\"><strong>Can the (a + b)<strong><strong><strong><strong><strong><sup>3<\/sup><\/strong><\/strong><\/strong><\/strong><\/strong> formula be used with negative values of &#8220;a&#8221; and &#8220;b&#8221;?<\/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-5-02e1b355-af95-4db1-9885-20cccdd56a63\">\n\n<p>Yes, the <strong>(a + b)<strong><strong><strong><strong><strong><strong><sup>3<\/sup><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong> formula can be used with negative values of &#8220;a&#8221; and &#8220;b.&#8221; The formula works regardless of the signs of the variables.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the (a + b)3 Formula? In algebra, the (a + b)3 formula allows us to find the cube of a binomial and helps us to simplify expressions.\u00a0 The formula for the cube of the sum of two terms, (a + b)3, can be expanded using the binomial theorem or by applying the distributive &#8230; <a title=\"$(A+B)^{3}$ Formula &#8211; Solved Examples, FAQS, Practice Problems\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/a-plus-b-cube-formula\" aria-label=\"More on $(A+B)^{3}$ Formula &#8211; Solved Examples, FAQS, Practice Problems\">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-34643","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\/34643","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=34643"}],"version-history":[{"count":4,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34643\/revisions"}],"predecessor-version":[{"id":34651,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34643\/revisions\/34651"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=34643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=34643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=34643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}