{"id":237217,"date":"2025-06-17T04:57:41","date_gmt":"2025-06-17T04:57:41","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=237217"},"modified":"2025-06-17T04:57:43","modified_gmt":"2025-06-17T04:57:43","slug":"what-is-9x2-30x-25","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/17\/what-is-9x2-30x-25\/","title":{"rendered":"what is 9&#215;2 \u2013 30x + 25"},"content":{"rendered":"\n<p>what is 9&#215;2 \u2013 30x + 25?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The expression <strong>9x\u00b2 \u2013 30x + 25<\/strong> is a quadratic trinomial. To simplify or factor this expression, let us try factoring it.<\/p>\n\n\n\n<p>We are given:<\/p>\n\n\n\n<p><strong>9x\u00b2 \u2013 30x + 25<\/strong><\/p>\n\n\n\n<p>This trinomial is in the standard quadratic form <strong>ax\u00b2 + bx + c<\/strong>, where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a = 9<\/li>\n\n\n\n<li>b = -30<\/li>\n\n\n\n<li>c = 25<\/li>\n<\/ul>\n\n\n\n<p>We need to check if this quadratic expression is a perfect square trinomial. A perfect square trinomial takes the form:<\/p>\n\n\n\n<p><strong>(mx \u2013 n)\u00b2 = m\u00b2x\u00b2 \u2013 2mnx + n\u00b2<\/strong><\/p>\n\n\n\n<p>Let\u2019s try:<\/p>\n\n\n\n<p><strong>(3x \u2013 5)\u00b2<\/strong><\/p>\n\n\n\n<p>Now expand this to see if it matches the original expression:<\/p>\n\n\n\n<p>(3x \u2013 5)(3x \u2013 5)<br>= 3x(3x) \u2013 3x(5) \u2013 5(3x) + 5(5)<br>= 9x\u00b2 \u2013 15x \u2013 15x + 25<br>= 9x\u00b2 \u2013 30x + 25<\/p>\n\n\n\n<p>Yes, it matches exactly.<\/p>\n\n\n\n<p><strong>Final Answer:<\/strong><br><strong>9x\u00b2 \u2013 30x + 25 = (3x \u2013 5)\u00b2<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>To understand the expression 9x\u00b2 \u2013 30x + 25, it helps to identify its structure. This is a quadratic trinomial, which means it has three terms and the highest exponent is two. The goal is often to factor it to find its roots or to simplify it for solving equations.<\/p>\n\n\n\n<p>Factoring involves expressing a quadratic trinomial as the product of two binomials. One method is checking whether the trinomial is a perfect square. This is a special case where both the first and last terms are perfect squares, and the middle term is twice the product of their square roots.<\/p>\n\n\n\n<p>In 9x\u00b2 \u2013 30x + 25, the first term, 9x\u00b2, is a perfect square because it is the square of 3x. The last term, 25, is a perfect square because it is the square of 5. Now check the middle term: 2 \u00d7 3x \u00d7 5 = 30x. Since the middle term is -30x, it matches -2ab from the square of a binomial. This confirms that the expression is a perfect square trinomial.<\/p>\n\n\n\n<p>So, we can write the expression as:<\/p>\n\n\n\n<p><strong>(3x \u2013 5)\u00b2<\/strong><\/p>\n\n\n\n<p>Factoring in this way helps solve quadratic equations, analyze graphs, and understand the behavior of functions. Recognizing perfect squares quickly is a useful algebra skill that saves time and simplifies more complex math problems.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-679.jpeg\" alt=\"\" class=\"wp-image-237218\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>what is 9&#215;2 \u2013 30x + 25? The Correct Answer and Explanation is: The expression 9x\u00b2 \u2013 30x + 25 is a quadratic trinomial. To simplify or factor this expression, let us try factoring it. We are given: 9x\u00b2 \u2013 30x + 25 This trinomial is in the standard quadratic form ax\u00b2 + bx + [&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-237217","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237217","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=237217"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237217\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=237217"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=237217"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=237217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}