{"id":269208,"date":"2025-07-24T11:51:48","date_gmt":"2025-07-24T11:51:48","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=269208"},"modified":"2025-07-24T11:51:50","modified_gmt":"2025-07-24T11:51:50","slug":"represent-algebraically","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/24\/represent-algebraically\/","title":{"rendered":"Represent algebraically"},"content":{"rendered":"\n

Represent algebraically: A number squared, increased by 15, is the same as the square of one more than the number. My teacher said x^2 + 15 = x^2 + 1 Is incorrect.<\/p>\n\n\n\n

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

To represent the statement “A number squared, increased by 15, is the same as the square of one more than the number” algebraically, let the number be represented by xxx.<\/p>\n\n\n\n

    \n
  1. First part of the statement<\/strong>: “A number squared, increased by 15” means the square of xxx plus 15, which is written as: x2+15x^2 + 15×2+15<\/li>\n\n\n\n
  2. Second part of the statement<\/strong>: “The square of one more than the number” means the square of x+1x + 1x+1. This is written as: (x+1)2(x + 1)^2(x+1)2<\/li>\n<\/ol>\n\n\n\n

    Now, according to the problem, these two expressions are equal. So, we set them equal to each other:x2+15=(x+1)2x^2 + 15 = (x + 1)^2×2+15=(x+1)2<\/p>\n\n\n\n

    Expanding the right-hand side:<\/h3>\n\n\n\n

    We need to expand (x+1)2(x + 1)^2(x+1)2. This is done by applying the binomial expansion:(x+1)2=x2+2x+1(x + 1)^2 = x^2 + 2x + 1(x+1)2=x2+2x+1<\/p>\n\n\n\n

    Setting up the equation:<\/h3>\n\n\n\n

    Substitute the expanded form of (x+1)2(x + 1)^2(x+1)2 back into the equation:x2+15=x2+2x+1x^2 + 15 = x^2 + 2x + 1×2+15=x2+2x+1<\/p>\n\n\n\n

    Simplifying the equation:<\/h3>\n\n\n\n

    Now, subtract x2x^2×2 from both sides to eliminate the x2x^2×2 terms:15=2x+115 = 2x + 115=2x+1<\/p>\n\n\n\n

    Solving for xxx:<\/h3>\n\n\n\n

    Next, subtract 1 from both sides:14=2×14 = 2×14=2x<\/p>\n\n\n\n

    Finally, divide by 2 to solve for xxx:x=7x = 7x=7<\/p>\n\n\n\n

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

    The correct algebraic representation of the problem is:x2+15=(x+1)2x^2 + 15 = (x + 1)^2×2+15=(x+1)2<\/p>\n\n\n\n

    The incorrect equation your teacher pointed out, x2+15=x2+1x^2 + 15 = x^2 + 1×2+15=x2+1, fails to account for the relationship between the number and one more than it, as it ignores the linear and constant terms that come from expanding (x+1)2(x + 1)^2(x+1)2. Therefore, the correct algebraic equation involves expanding (x+1)2(x + 1)^2(x+1)2 as shown.<\/p>\n\n\n\n

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

    Represent algebraically: A number squared, increased by 15, is the same as the square of one more than the number. My teacher said x^2 + 15 = x^2 + 1 Is incorrect. The Correct Answer and Explanation is: To represent the statement “A number squared, increased by 15, is the same as the square of […]<\/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-269208","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/269208","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=269208"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/269208\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=269208"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=269208"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=269208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}