To factor the expression x2\u221225x^2 – 25×2\u221225, we recognize that it is a difference of squares<\/strong>. The general formula for factoring a difference of squares is: a2\u2212b2=(a+b)(a\u2212b)a^2 – b^2 = (a + b)(a – b)a2\u2212b2=(a+b)(a\u2212b)<\/p>\n\n\n\n In your case, the expression is: x2\u221225x^2 – 25×2\u221225<\/p>\n\n\n\n Here, x2x^2×2 is a perfect square (x2=x2x^2 = x^2×2=x2) and 25 is also a perfect square (25=5225 = 5^225=52).<\/p>\n\n\n\n We can now apply the difference of squares formula, where: a=xandb=5a = x \\quad \\text{and} \\quad b = 5a=xandb=5<\/p>\n\n\n\n Thus, the factored form of x2\u221225x^2 – 25×2\u221225 is: (x+5)(x\u22125)(x + 5)(x – 5)(x+5)(x\u22125)<\/p>\n\n\n\n The difference of squares formula works because of how squares behave mathematically. Any expression of the form a2\u2212b2a^2 – b^2a2\u2212b2 can be factored into the product of two binomials: (a+b)(a + b)(a+b) and (a\u2212b)(a – b)(a\u2212b).<\/p>\n\n\n\n In this specific case, x2\u221225x^2 – 25×2\u221225 can be rewritten as: x2\u221252x^2 – 5^2×2\u221252<\/p>\n\n\n\n This fits the difference of squares pattern, and so we factor it as: (x+5)(x\u22125)(x + 5)(x – 5)(x+5)(x\u22125)<\/p>\n\n\n\n This factorization gives us two factors, x+5x + 5x+5 and x\u22125x – 5x\u22125, which are the roots of the equation x2\u221225=0x^2 – 25 = 0x2\u221225=0. To check the factorization, you can expand (x+5)(x\u22125)(x + 5)(x – 5)(x+5)(x\u22125) back: (x+5)(x\u22125)=x2\u22125x+5x\u221225=x2\u221225(x + 5)(x – 5) = x^2 – 5x + 5x – 25 = x^2 – 25(x+5)(x\u22125)=x2\u22125x+5x\u221225=x2\u221225<\/p>\n\n\n\n So, the factorization is correct.<\/p>\n\n\n\n The factored form of x2\u221225x^2 – 25×2\u221225 is: (x+5)(x\u22125)(x + 5)(x – 5)(x+5)(x\u22125)<\/p>\n\n\n\n This method is a standard approach for factoring quadratic expressions that are a difference of squares.<\/p>\n\n\n\n What is the anwer of X2 – 25 FACTOR The Correct Answer and Explanation is: To factor the expression x2\u221225x^2 – 25×2\u221225, we recognize that it is a difference of squares. The general formula for factoring a difference of squares is: a2\u2212b2=(a+b)(a\u2212b)a^2 – b^2 = (a + b)(a – b)a2\u2212b2=(a+b)(a\u2212b) In your case, the expression […]<\/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-255955","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/255955","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=255955"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/255955\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=255955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=255955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=255955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
Conclusion:<\/h3>\n\n\n\n
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<\/figure>\n","protected":false},"excerpt":{"rendered":"