{"id":144349,"date":"2024-09-24T14:19:57","date_gmt":"2024-09-24T14:19:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=144349"},"modified":"2024-09-24T14:19:59","modified_gmt":"2024-09-24T14:19:59","slug":"which-is-a-difference-of-cubes","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/09\/24\/which-is-a-difference-of-cubes\/","title":{"rendered":"Which is a difference of cubes"},"content":{"rendered":"\n

Which is a difference of cubes?<\/p>\n\n\n\n

x6 \u2013 27
x15 \u2013 36
x16 \u2013 64
x5 \u2013 125<\/p>\n\n\n\n

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

A difference of cubes is an algebraic expression that can be represented in the form ( a^3 – b^3 ), which can be factored using the formula:<\/p>\n\n\n\n

[
a^3 – b^3 = (a – b)(a^2 + ab + b^2)
]<\/p>\n\n\n\n

To determine which of the expressions provided is a difference of cubes, we can analyze each one:<\/p>\n\n\n\n

    \n
  1. ( x^6 – 27 )<\/strong>:<\/li>\n<\/ol>\n\n\n\n
      \n
    • This can be rewritten as ( (x^2)^3 – 3^3 ).<\/li>\n\n\n\n
    • Here, ( a = x^2 ) and ( b = 3 ), so it is a difference of cubes.<\/li>\n<\/ul>\n\n\n\n
        \n
      1. ( x^{15} – 36 )<\/strong>:<\/li>\n<\/ol>\n\n\n\n
          \n
        • This does not fit the form ( a^3 – b^3 ) because ( 36 ) is not a perfect cube.<\/li>\n\n\n\n
        • The cube root of ( 36 ) is not an integer.<\/li>\n<\/ul>\n\n\n\n
            \n
          1. ( x^{16} – 64 )<\/strong>:<\/li>\n<\/ol>\n\n\n\n
              \n
            • This can be rewritten as ( (x^{16\/3})^3 – 4^3 ).<\/li>\n\n\n\n
            • However, ( x^{16\/3} ) is not a simple term like ( x^n ), so this is not a standard difference of cubes.<\/li>\n<\/ul>\n\n\n\n
                \n
              1. ( x^5 – 125 )<\/strong>:<\/li>\n<\/ol>\n\n\n\n
                  \n
                • This can be rewritten as ( x^5 – (5)^3 ).<\/li>\n\n\n\n
                • Here, ( a = x^{5\/3} ) and ( b = 5 ), which again complicates it.<\/li>\n<\/ul>\n\n\n\n

                  Conclusion<\/h3>\n\n\n\n

                  The only expression among the four provided that clearly fits the difference of cubes format is ( x^6 – 27 )<\/strong>. This expression can be factored as:<\/p>\n\n\n\n

                  [
                  x^6 – 27 = (x^2 – 3)(x^4 + 3x^2 + 9)
                  ]<\/p>\n\n\n\n

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

                  In algebra, recognizing patterns such as the difference of cubes is essential for simplifying expressions and solving equations. The structure ( a^3 – b^3 ) represents the difference between two cubes, where each component can be expressed as a cubic term. The factorization not only provides a simpler form but also reveals the roots of the equation when set to zero. Understanding how to manipulate these forms is a fundamental skill in algebra that has applications across calculus, physics, engineering, and beyond.<\/p>\n","protected":false},"excerpt":{"rendered":"

                  Which is a difference of cubes? x6 \u2013 27×15 \u2013 36×16 \u2013 64×5 \u2013 125 The Correct Answer and Explanation is : A difference of cubes is an algebraic expression that can be represented in the form ( a^3 – b^3 ), which can be factored using the formula: [a^3 – b^3 = (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-144349","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144349","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=144349"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/144349\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=144349"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=144349"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=144349"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}