{"id":236409,"date":"2025-06-16T08:27:49","date_gmt":"2025-06-16T08:27:49","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=236409"},"modified":"2025-06-16T08:27:51","modified_gmt":"2025-06-16T08:27:51","slug":"formula-of-a-plus-b-whole-cube-and-a-minus-b-whole-cube","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/formula-of-a-plus-b-whole-cube-and-a-minus-b-whole-cube\/","title":{"rendered":"Formula of a plus b whole cube and a minus b whole cube"},"content":{"rendered":"\n<p>Formula of a plus b whole cube and a minus b whole cube<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h6 class=\"wp-block-heading\">ChatGPT said:<\/h6>\n\n\n\n<p><strong>Correct Answer:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(a+b)3=a3+3a2b+3ab2+b3(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3(a+b)3=a3+3a2b+3ab2+b3<\/li>\n\n\n\n<li>(a\u2212b)3=a3\u22123a2b+3ab2\u2212b3(a &#8211; b)^3 = a^3 &#8211; 3a^2b + 3ab^2 &#8211; b^3(a\u2212b)3=a3\u22123a2b+3ab2\u2212b3<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation<\/strong><\/p>\n\n\n\n<p>The expressions (a+b)3(a + b)^3(a+b)3 and (a\u2212b)3(a &#8211; b)^3(a\u2212b)3 are examples of binomial cubes. These represent the cube of a binomial \u2014 an algebraic expression that has two terms. Cubing a binomial means multiplying the expression by itself three times.<\/p>\n\n\n\n<p>To expand (a+b)3(a + b)^3(a+b)3, the expression becomes:(a+b)(a+b)(a+b)(a + b)(a + b)(a + b)(a+b)(a+b)(a+b)<\/p>\n\n\n\n<p>Using the distributive property (also called the FOIL method for two binomials), the first two binomials multiply to form:(a+b)(a+b)=a2+2ab+b2(a + b)(a + b) = a^2 + 2ab + b^2(a+b)(a+b)=a2+2ab+b2<\/p>\n\n\n\n<p>Multiplying this result by (a+b)(a + b)(a+b) again:(a2+2ab+b2)(a+b)=a3+3a2b+3ab2+b3(a^2 + 2ab + b^2)(a + b) = a^3 + 3a^2b + 3ab^2 + b^3(a2+2ab+b2)(a+b)=a3+3a2b+3ab2+b3<\/p>\n\n\n\n<p>This result gives the expanded form of (a+b)3(a + b)^3(a+b)3.<\/p>\n\n\n\n<p>Similarly, for (a\u2212b)3(a &#8211; b)^3(a\u2212b)3, the binomial cube expands as:(a\u2212b)(a\u2212b)(a\u2212b)(a &#8211; b)(a &#8211; b)(a &#8211; b)(a\u2212b)(a\u2212b)(a\u2212b)<\/p>\n\n\n\n<p>The first part becomes:(a\u2212b)(a\u2212b)=a2\u22122ab+b2(a &#8211; b)(a &#8211; b) = a^2 &#8211; 2ab + b^2(a\u2212b)(a\u2212b)=a2\u22122ab+b2<\/p>\n\n\n\n<p>Multiplying by (a\u2212b)(a &#8211; b)(a\u2212b) gives:(a2\u22122ab+b2)(a\u2212b)=a3\u22123a2b+3ab2\u2212b3(a^2 &#8211; 2ab + b^2)(a &#8211; b) = a^3 &#8211; 3a^2b + 3ab^2 &#8211; b^3(a2\u22122ab+b2)(a\u2212b)=a3\u22123a2b+3ab2\u2212b3<\/p>\n\n\n\n<p>This is the expanded form of (a\u2212b)3(a &#8211; b)^3(a\u2212b)3.<\/p>\n\n\n\n<p>Both formulas follow a clear pattern:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The first and last terms are the cubes of the original binomial components.<\/li>\n\n\n\n<li>The middle terms involve combinations of a2ba^2ba2b and ab2ab^2ab2, scaled by a factor of 3.<\/li>\n\n\n\n<li>The signs alternate depending on whether the original expression involves addition or subtraction.<\/li>\n<\/ul>\n\n\n\n<p>These identities are fundamental in algebra and are often used in factoring, polynomial expansion, and solving equations.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-185.jpeg\" alt=\"\" class=\"wp-image-236411\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Formula of a plus b whole cube and a minus b whole cube The Correct Answer and Explanation is: ChatGPT said: Correct Answer: Explanation The expressions (a+b)3(a + b)^3(a+b)3 and (a\u2212b)3(a &#8211; b)^3(a\u2212b)3 are examples of binomial cubes. These represent the cube of a binomial \u2014 an algebraic expression that has two terms. Cubing a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-236409","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236409","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=236409"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236409\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=236409"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=236409"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=236409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}