{"id":153835,"date":"2024-10-13T18:35:10","date_gmt":"2024-10-13T18:35:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=153835"},"modified":"2024-10-13T18:35:13","modified_gmt":"2024-10-13T18:35:13","slug":"factor-completely-9x2-%e2%88%92-25","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/13\/factor-completely-9x2-%e2%88%92-25\/","title":{"rendered":"Factor completely 9&#215;2 \u2212 25"},"content":{"rendered":"\n<p>Factor completely 9&#215;2 \u2212 25.<\/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 factor the expression (9x^2 &#8211; 25), we first recognize that this is a difference of squares. A difference of squares can be expressed in the form (a^2 &#8211; b^2), which factors as ((a &#8211; b)(a + b)).<\/p>\n\n\n\n<p>In the expression (9x^2 &#8211; 25):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The term (9x^2) can be rewritten as ((3x)^2).<\/li>\n\n\n\n<li>The term (25) can be rewritten as (5^2).<\/li>\n<\/ul>\n\n\n\n<p>Thus, we can identify (a) and (b) as follows:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(a = 3x)<\/li>\n\n\n\n<li>(b = 5)<\/li>\n<\/ul>\n\n\n\n<p>Substituting these values into the difference of squares formula, we get:<\/p>\n\n\n\n<p>[<br>9x^2 &#8211; 25 = (3x)^2 &#8211; 5^2 = (3x &#8211; 5)(3x + 5)<br>]<\/p>\n\n\n\n<p>This expression is now fully factored.<\/p>\n\n\n\n<p>To understand why this method works, let&#8217;s break it down:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identifying Squares<\/strong>: The key to factoring a difference of squares is recognizing the two squared terms. In our case, (9x^2) is a perfect square because it can be expressed as ((3x)^2), and (25) is a perfect square because it equals (5^2).<\/li>\n\n\n\n<li><strong>Applying the Formula<\/strong>: Once we identify the squares, we can apply the difference of squares formula directly. This is a standard factoring technique in algebra and is very useful for simplifying expressions and solving equations.<\/li>\n\n\n\n<li><strong>Verification<\/strong>: To ensure our factorization is correct, we can use the distributive property (also known as the FOIL method for binomials) to expand ((3x &#8211; 5)(3x + 5)):<\/li>\n<\/ol>\n\n\n\n<p>[<br>(3x &#8211; 5)(3x + 5) = 3x \\cdot 3x + 3x \\cdot 5 &#8211; 5 \\cdot 3x &#8211; 5 \\cdot 5 = 9x^2 &#8211; 25<br>]<\/p>\n\n\n\n<p>This matches our original expression, confirming that the factorization is indeed correct.<\/p>\n\n\n\n<p>In conclusion, the complete factorization of (9x^2 &#8211; 25) is ((3x &#8211; 5)(3x + 5)).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Factor completely 9&#215;2 \u2212 25. The Correct Answer and Explanation is : To factor the expression (9x^2 &#8211; 25), we first recognize that this is a difference of squares. A difference of squares can be expressed in the form (a^2 &#8211; b^2), which factors as ((a &#8211; b)(a + b)). In the expression (9x^2 &#8211; [&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-153835","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153835","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=153835"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/153835\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=153835"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=153835"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=153835"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}