{"id":3392,"date":"2014-01-11T18:55:23","date_gmt":"2014-01-11T18:55:23","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=3392"},"modified":"2017-09-09T01:00:08","modified_gmt":"2017-09-09T01:00:08","slug":"math-factoring-sum-of-cubes","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-factoring-sum-of-cubes\/","title":{"rendered":"Math:  factoring sum of cubes"},"content":{"rendered":"<h1>Tutoring high school math, you rarely see this; it comes up often, however, in calculus. \u00a0The tutor offers a light treatment.<\/h1>\n<p>How do you factor x^3 + 125? You need the following formula:<\/p>\n<p>a^3 + b^3 = (a + b)(a^2 &#8211; ab + b^2)<\/p>\n<p>Of course, 125=5^3. Carefully substituting x for a and 5 for b, we arrive at<\/p>\n<p>x^3 + 125=(x+5)(x^2-5x+25)<\/p>\n<p>What about factoring 8x^3+1?<\/p>\n<p>We need to realize that, really,<\/p>\n<p>8x^3+1=(2x)^3 + 1^3<\/p>\n<p>Substituting 2x for a and 1 for b in the formula, we arrive at<\/p>\n<p>8x^3+1=(2x+1)((2x)^2 &#8211; 2x(1) + 1^2)=(2x+1)(4x^2 &#8211; 2x + 1)<\/p>\n<p>For a hint about factoring the difference of cubes, please come back soon:)<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tutoring high school math, you rarely see this; it comes up often, however, in calculus. \u00a0The tutor offers a light treatment. How do you factor x^3 + 125? You need the following formula: a^3 + b^3 = (a + b)(a^2 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-factoring-sum-of-cubes\/\"> <span class=\"screen-reader-text\">Math:  factoring sum of cubes<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[35,65],"class_list":["post-3392","post","type-post","status-publish","format-standard","hentry","category-math","tag-factoring","tag-sum-of-cubes"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/3392","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=3392"}],"version-history":[{"count":19,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/3392\/revisions"}],"predecessor-version":[{"id":23514,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/3392\/revisions\/23514"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=3392"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=3392"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=3392"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}