{"id":153395,"date":"2024-10-13T04:55:28","date_gmt":"2024-10-13T04:55:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=153395"},"modified":"2024-10-13T04:55:30","modified_gmt":"2024-10-13T04:55:30","slug":"how-would-the-expression-x%c2%b3-8-be-rewritten-using-the-sum-of-cubes","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/13\/how-would-the-expression-x%c2%b3-8-be-rewritten-using-the-sum-of-cubes\/","title":{"rendered":"How would the expression ( x\u00b3 + 8 ) be rewritten using the sum of cubes"},"content":{"rendered":"\n<p>How would the expression ( x\u00b3 + 8 ) be rewritten using the sum of cubes?<br>a. ( (x\u00b2)(x\u00b2 &#8211; 2x\u2074) )<br>b. ( (x\u00b2)(x\u00b2 &#8211; 2x &#8211; 4) )<br>c. ( (x &#8211; 2)(x\u00b2 &#8211; 2x\u2074) )<br>d. ( (x\u00b2)(x\u00b2 + 2x &#8211; 4) )<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To rewrite the expression ( x^3 + 8 ) using the sum of cubes formula, we need to recognize that both terms in the expression are perfect cubes.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Recognizing the Sum of Cubes Formula<\/h3>\n\n\n\n<p>The general sum of cubes formula is:<br>[<br>a^3 + b^3 = (a + b)(a^2 &#8211; ab + b^2)<br>]<\/p>\n\n\n\n<p>In this case:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( x^3 ) is ( a^3 ) where ( a = x )<\/li>\n\n\n\n<li>( 8 ) is ( b^3 ) where ( b = 2 ), since ( 2^3 = 8 )<\/li>\n<\/ul>\n\n\n\n<p>So, we can apply the sum of cubes formula with ( a = x ) and ( b = 2 ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Applying the Formula<\/h3>\n\n\n\n<p>Using the sum of cubes formula:<br>[<br>x^3 + 8 = (x + 2)\\left(x^2 &#8211; (x)(2) + 2^2\\right)<br>]<br>This simplifies as:<br>[<br>x^3 + 8 = (x + 2)(x^2 &#8211; 2x + 4)<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Matching the Choices<\/h3>\n\n\n\n<p>From the provided options, none of the choices perfectly match the expression ( (x + 2)(x^2 &#8211; 2x + 4) ). However, based on what we derived using the sum of cubes, the correct form is the simplified expression above.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Correct Formulation:<\/h3>\n\n\n\n<p>The correct answer is <strong>none of the options<\/strong> exactly as written. The correct expression should be ( (x + 2)(x^2 &#8211; 2x + 4) ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation of the Process:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The term ( x^3 ) is a cube of ( x ) and ( 8 ) is a cube of ( 2 ).<\/li>\n\n\n\n<li>Using the sum of cubes formula helps break down the expression into a product of two factors: ( (x + 2) ) and ( (x^2 &#8211; 2x + 4) ).<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>How would the expression ( x\u00b3 + 8 ) be rewritten using the sum of cubes?a. ( (x\u00b2)(x\u00b2 &#8211; 2x\u2074) )b. ( (x\u00b2)(x\u00b2 &#8211; 2x &#8211; 4) )c. ( (x &#8211; 2)(x\u00b2 &#8211; 2x\u2074) )d. ( (x\u00b2)(x\u00b2 + 2x &#8211; 4) ) The Correct Answer and Explanation is : To rewrite the expression ( x^3 [&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-153395","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153395","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=153395"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153395\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=153395"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=153395"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=153395"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}