{"id":236414,"date":"2025-06-16T08:30:26","date_gmt":"2025-06-16T08:30:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=236414"},"modified":"2025-06-16T08:30:28","modified_gmt":"2025-06-16T08:30:28","slug":"tell-me-the-formula-of-ab-whole-cube","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/tell-me-the-formula-of-ab-whole-cube\/","title":{"rendered":"Tell me the formula of (a+b) whole cube."},"content":{"rendered":"\n

Tell me the formula of (a+b) whole cube. I can’t remember it\u2026<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Formula:<\/h3>\n\n\n\n

(a + b)\u00b3 = a\u00b3 + 3a\u00b2b + 3ab\u00b2 + b\u00b3<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/h3>\n\n\n\n

The expansion of the expression (a+b)3(a + b)^3(a+b)3 follows the algebraic identity used to multiply a binomial three times. This means multiplying (a+b)(a + b)(a+b) by itself three times:
(a+b)(a+b)(a+b)(a + b)(a + b)(a + b)(a+b)(a+b)(a+b)<\/p>\n\n\n\n

To understand the structure, begin by first multiplying the first two binomials:
(a+b)(a+b)=a2+2ab+b2(a + b)(a + b) = a^2 + 2ab + b^2(a+b)(a+b)=a2+2ab+b2
Then, multiply the result by the third (a+b)(a + b)(a+b) term:
(a2+2ab+b2)(a+b)(a^2 + 2ab + b^2)(a + b)(a2+2ab+b2)(a+b)<\/p>\n\n\n\n

Now distribute each term in the first trinomial over the second binomial:<\/p>\n\n\n\n

    \n
  • a2\u22c5a=a3a^2 \\cdot a = a^3a2\u22c5a=a3<\/li>\n\n\n\n
  • a2\u22c5b=a2ba^2 \\cdot b = a^2ba2\u22c5b=a2b<\/li>\n\n\n\n
  • 2ab\u22c5a=2a2b2ab \\cdot a = 2a^2b2ab\u22c5a=2a2b<\/li>\n\n\n\n
  • 2ab\u22c5b=2ab22ab \\cdot b = 2ab^22ab\u22c5b=2ab2<\/li>\n\n\n\n
  • b2\u22c5a=ab2b^2 \\cdot a = ab^2b2\u22c5a=ab2<\/li>\n\n\n\n
  • b2\u22c5b=b3b^2 \\cdot b = b^3b2\u22c5b=b3<\/li>\n<\/ul>\n\n\n\n

    Now combine like terms:<\/p>\n\n\n\n

      \n
    • a3a^3a3<\/li>\n\n\n\n
    • a2b+2a2b=3a2ba^2b + 2a^2b = 3a^2ba2b+2a2b=3a2b<\/li>\n\n\n\n
    • ab2+2ab2=3ab2ab^2 + 2ab^2 = 3ab^2ab2+2ab2=3ab2<\/li>\n\n\n\n
    • b3b^3b3<\/li>\n<\/ul>\n\n\n\n

      Final result:
      (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<\/p>\n\n\n\n

      This expansion illustrates the symmetry in binomial cube identities. Each term reflects a combination of the powers of aaa and bbb that add up to 3. The coefficients (1, 3, 3, 1) match the third row of Pascal\u2019s Triangle, which provides a pattern for binomial expansions. This identity is foundational in algebra and simplifies solving problems involving cubic expressions in both pure mathematics and applied contexts such as physics and engineering.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Tell me the formula of (a+b) whole cube. I can’t remember it\u2026 The Correct Answer and Explanation is: Formula: (a + b)\u00b3 = a\u00b3 + 3a\u00b2b + 3ab\u00b2 + b\u00b3 Explanation: The expansion of the expression (a+b)3(a + b)^3(a+b)3 follows the algebraic identity used to multiply a binomial three times. This means multiplying (a+b)(a + […]<\/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-236414","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236414","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=236414"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236414\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=236414"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=236414"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=236414"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}