Which statement is true about the polynomial 3x2y2 \u2212 5xy2 \u2212 3x2y2 2×2 after it has been fully simplified?<\/p>\n\n\n\n
The correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To simplify the polynomial (3x^2y^2 – 5xy^2 – 3x^2y^2 + 2x^2), let’s follow these steps:<\/p>\n\n\n\n We have two pairs of like terms that can be simplified. Like terms are terms that have the same variables raised to the same powers.<\/p>\n\n\n\n Now, simplify:<\/p>\n\n\n\n [ So, the polynomial reduces to:<\/p>\n\n\n\n [ After simplifying the like terms, the final polynomial is:<\/p>\n\n\n\n [ In this polynomial, we started by identifying like terms\u2014terms that share both the same variables and the same exponents for those variables. The first and third terms, (3x^2y^2) and (-3x^2y^2), cancel each other out because their coefficients sum to zero. This leaves us with two terms that are not alike: (-5xy^2) and (2x^2). These terms cannot be combined because they involve different variables or different powers of those variables.<\/p>\n\n\n\n Thus, after combining like terms, the polynomial simplifies to (2x^2 – 5xy^2). This expression represents the simplest form of the original polynomial, as no further combination or factoring is possible.<\/p>\n\n\n\n The true statement about the polynomial (3x^2y^2 – 5xy^2 – 3x^2y^2 + 2x^2) is that, when fully simplified, it becomes (2x^2 – 5xy^2).<\/p>\n","protected":false},"excerpt":{"rendered":" Which statement is true about the polynomial 3x2y2 \u2212 5xy2 \u2212 3x2y2 2×2 after it has been fully simplified? The correct Answer and Explanation is: To simplify the polynomial (3x^2y^2 – 5xy^2 – 3x^2y^2 + 2x^2), let’s follow these steps: Step 1: Combine Like Terms We have two pairs of like terms that can be […]<\/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-149981","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149981","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=149981"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149981\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=149981"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=149981"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=149981"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Combine Like Terms<\/h3>\n\n\n\n
\n
3x^2y^2 – 3x^2y^2 = 0
]<\/p>\n\n\n\n
-5xy^2 + 2x^2
]<\/p>\n\n\n\nStep 2: Final Simplified Polynomial<\/h3>\n\n\n\n
2x^2 – 5xy^2
]<\/p>\n\n\n\nExplanation of the Simplification Process<\/h3>\n\n\n\n
Conclusion<\/h3>\n\n\n\n