{"id":10892,"date":"2012-07-16T09:00:52","date_gmt":"2012-07-16T16:00:52","guid":{"rendered":"https:\/\/magoosh.com\/gre\/?p=10892"},"modified":"2019-07-16T11:39:03","modified_gmt":"2019-07-16T18:39:03","slug":"gre-quant-the-difference-of-squares","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gre\/gre-quant-the-difference-of-squares\/","title":{"rendered":"GRE Quant: The Difference of Squares"},"content":{"rendered":"<p>If you\u2019ve been studying GRE for some time, you\u2019ve very likely encountered the following:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_990.5_9773ebb0d678852a428bd1c08f0db6f7.png\" style=\"vertical-align:-9.5px; display: inline-block ;\" alt=\"x^2 - y^2 = (x - y)(x+ y) = 0\" title=\"x^2 - y^2 = (x - y)(x+ y) = 0\"\/>.<\/p>\n<p>You may, however, only seen the following equation in the context of algebra. Nevertheless, the formula above applies to number properties. Let\u2019s take a look.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_983.5_754e8735082ffbe24082c81b12e4ab08.png\" style=\"vertical-align:-16.5px; display: inline-block ;\" alt=\"(16^2 - 15^2)(15^2 - 14^2)\" title=\"(16^2 - 15^2)(15^2 - 14^2)\"\/><\/p>\n<p>While you may be tempted to make a mad dash at it, calculating each of the squares, there is an easier way. Think of the \u201816\u2019 as the \u2018x\u2019 and the \u201815\u2019 as the \u2018y\u2019. Using the equation above we get:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_983.5_e1a48ff46ef3d4ce2c06dc8b54af5bed.png\" style=\"vertical-align:-16.5px; display: inline-block ;\" alt=\"(16^2 - 15^2) = (16 - 15) (16 + 15) = 31\" title=\"(16^2 - 15^2) = (16 - 15) (16 + 15) = 31\"\/>.<\/p>\n<p>Wow, that was much easier than figuring out the squares of both \u201816\u2019 and \u201915.\u2019 Now, let\u2019s try it for the second pair:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_983.5_677b86ff9b797d6cf920c594bc5a9a16.png\" style=\"vertical-align:-16.5px; display: inline-block ;\" alt=\"(15^2\u00a0 - 14^2) = (15 - 14) (15 + 14) = 29\" title=\"(15^2\u00a0 - 14^2) = (15 - 14) (15 + 14) = 29\"\/><\/p>\n<p>That leaves us with (29)(31). I know, you may be balking at my nifty little formula, thinking you still need to do some tedious multiplication. But despair not! We can still use the difference of squares formula:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_990.5_048175dc5497bf5622a8d439fcdd7dbb.png\" style=\"vertical-align:-9.5px; display: inline-block ;\" alt=\"X^2 - 1 = (x - 1)(x + 1)\" title=\"X^2 - 1 = (x - 1)(x + 1)\"\/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_991_9d0c0741c0c45906abe2b2cf3c2c7353.png\" style=\"vertical-align:-9px; display: inline-block ;\" alt=\"30^2 - 1 = (30 - 1)(30 + 1) = (31)(29)\" title=\"30^2 - 1 = (30 - 1)(30 + 1) = (31)(29)\"\/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_993_cbe168d4321dfae58bd2aee88d0400c9.png\" style=\"vertical-align:-7px; display: inline-block ;\" alt=\"30^2\" title=\"30^2\"\/> is simply 3 x 3 add two zeroes: 900. Then we subtract the one and we get 899.<\/p>\n<p>Next our two practice questions. The first question is not very different from the one above. The second one is more challenging and involves exponents.<\/p>\n<p>&nbsp;<\/p>\n<h2>Practice Questions<\/h2>\n<p>1. <img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_983.5_0360e97f92ce0b4aa2326c870500b4e8.png\" style=\"vertical-align:-16.5px; display: inline-block ;\" alt=\"(20^2 - 18^2) - (19^2 - 17^2)\" title=\"(20^2 - 18^2) - (19^2 - 17^2)\"\/>?<\/p>\n<ol>\n<li>4<\/li>\n<li>36<\/li>\n<li>38<\/li>\n<li>76<\/li>\n<li>224<\/li>\n<\/ol>\n<p>2. <img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_977_3b7e25d769357edd805975612175d398.png\" style=\"vertical-align:-23px; display: inline-block ;\" alt=\"{4^8 - 3^8}\/{4^4 + 3^4}\" title=\"{4^8 - 3^8}\/{4^4 + 3^4}\"\/>=<\/p>\n<ol>\n<li>7<\/li>\n<li>25<\/li>\n<li>156<\/li>\n<li>175<\/li>\n<li>216<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<h2>Explanations:<\/h2>\n<p><strong>\u00a0<\/strong>1. <img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_983.5_79e5f6d8625f147c6ebc9cd9facec56d.png\" style=\"vertical-align:-16.5px; display: inline-block ;\" alt=\"(20^2 - 18^2) = (20 - 18)(20 + 18) = 76\" title=\"(20^2 - 18^2) = (20 - 18)(20 + 18) = 76\"\/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_983.5_91c885ab3604170685c2331ed2a22b68.png\" style=\"vertical-align:-16.5px; display: inline-block ;\" alt=\"(19^2 - 17^2) = (19 - 17)(19 + 17) = 72\u00a0\" title=\"(19^2 - 17^2) = (19 - 17)(19 + 17) = 72\u00a0\"\/><\/p>\n<p>76 \u2013 72 = 4, Answer (A).<\/p>\n<p>2. <img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_977_a905d20c57c9fd8e65b1460c379d9d83.png\" style=\"vertical-align:-23px; display: inline-block ;\" alt=\"{4^8 - 3^8}\/{4^4 + 3^4}=\" title=\"{4^8 - 3^8}\/{4^4 + 3^4}=\"\/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_977_69d177794733a8b18891c3a83a989383.png\" style=\"vertical-align:-23px; display: inline-block ;\" alt=\"{(4^4 - 3^4)(4^4 + 3^4)}\/{4^4 + 3^4}\" title=\"{(4^4 - 3^4)(4^4 + 3^4)}\/{4^4 + 3^4}\"\/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/magoosh.com\/gre\/wp-content\/plugins\/wpmathpub\/phpmathpublisher\/img\/math_983.5_f409aef322b734e6ec92ded79e5b6113.png\" style=\"vertical-align:-16.5px; display: inline-block ;\" alt=\"(4^4 - 3^4) = (4^2 - 3^2)(4^2 + 3^2) = (7)(25) = 175\" title=\"(4^4 - 3^4) = (4^2 - 3^2)(4^2 + 3^2) = (7)(25) = 175\"\/>.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>If you\u2019ve been studying GRE for some time, you\u2019ve very likely encountered the following: . You may, however, only seen the following equation in the context of algebra. Nevertheless, the formula above applies to number properties. Let\u2019s take a look. While you may be tempted to make a mad dash at it, calculating each of [&hellip;]<\/p>\n","protected":false},"author":10,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25,10764],"tags":[],"ppma_author":[12264],"class_list":["post-10892","post","type-post","status-publish","format-standard","hentry","category-math","category-math-practice"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>GRE Quant: The Difference of Squares - Magoosh Blog \u2014 GRE\u00ae Test<\/title>\n<meta name=\"description\" content=\"Magoosh\u2019s expert Chris Lele explains how to calculate the difference of squares on the GRE Quant using a simple equation.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/magoosh.com\/gre\/gre-quant-the-difference-of-squares\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GRE Quant: The Difference of Squares\" \/>\n<meta property=\"og:description\" content=\"Magoosh\u2019s expert Chris Lele explains how to calculate the difference of squares on the GRE Quant using a simple equation.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gre\/gre-quant-the-difference-of-squares\/\" \/>\n<meta property=\"og:site_name\" content=\"Magoosh Blog \u2014 GRE\u00ae Test\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Magoosh\/\" \/>\n<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/ChrisLeleMagoosh1\/\" \/>\n<meta property=\"article:published_time\" content=\"2012-07-16T16:00:52+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-07-16T18:39:03+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/magoosh.com\/gre\/files\/2016\/09\/Magoosh-Facebook-Default-Pic.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"628\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Chris Lele\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@chrismagoosh\" \/>\n<meta name=\"twitter:site\" content=\"@MagooshGRE\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Chris Lele\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/magoosh.com\/gre\/gre-quant-the-difference-of-squares\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gre\/gre-quant-the-difference-of-squares\/\"},\"author\":{\"name\":\"Chris Lele\",\"@id\":\"https:\/\/magoosh.com\/gre\/#\/schema\/person\/3b6630b4f786513b81a860849cffd546\"},\"headline\":\"GRE Quant: The Difference of Squares\",\"datePublished\":\"2012-07-16T16:00:52+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gre\/gre-quant-the-difference-of-squares\/\"},\"wordCount\":253,\"commentCount\":12,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gre\/#organization\"},\"articleSection\":[\"GRE Math\",\"Shorter GRE Math Practice\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/gre\/gre-quant-the-difference-of-squares\/\",\"url\":\"https:\/\/magoosh.com\/gre\/gre-quant-the-difference-of-squares\/\",\"name\":\"GRE Quant: The Difference of Squares - 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He's been quoted as a subject expert in many publications, including<a href=\"https:\/\/www.usnews.com\/education\/best-colleges\/slideshows\/10-test-prep-tips-for-sat-and-act-takers\" rel=\"noopener noreferrer\"> US News<\/a>,<a href=\"https:\/\/www.mba.com\/exams-and-exam-prep\/gmat-exam\/why-take-the-gmat-in-2021-when-many-schools-are-test-optional\" rel=\"noopener noreferrer\"> GMAC<\/a>, and<a href=\"https:\/\/www.businessbecause.com\/news\/gmat\/3263\/mba-admissions-gre-challenges-gmat\" rel=\"noopener noreferrer\"> Business Because<\/a>.\r\n"}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/posts\/10892","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/comments?post=10892"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/posts\/10892\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/media?parent=10892"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/categories?post=10892"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/tags?post=10892"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gre\/wp-json\/wp\/v2\/ppma_author?post=10892"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}