{"id":3411,"date":"2014-01-14T21:36:12","date_gmt":"2014-01-14T21:36:12","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=3411"},"modified":"2017-09-09T00:55:49","modified_gmt":"2017-09-09T00:55:49","slug":"math-factoring-difference-of-cubes","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-factoring-difference-of-cubes\/","title":{"rendered":"Math:  factoring difference of cubes"},"content":{"rendered":"<h1>The math tutor continues with factoring cubes. \u00a0Tutoring calculus, this formula is another standby.<\/h1>\n<p>Let&#8217;s turn to factoring x^3 &#8211; 64. Realizing that 64=4^3, you actually are facing x^3-4^3<\/p>\n<p>You need the formula<\/p>\n<p>a^3 &#8211; b^3=(a-b)(a^2 + ab + b^2)<\/p>\n<p>For x^3-64, we substitute x for a and 4 for b. We arrive at<\/p>\n<p>x^3-64=(x-4)(x^2+x(4)+16)=(x-4)(x^2+4x+16)<\/p>\n<p>What about factoring 343x^6-8y^3? Since 343=7^3 and 8=2^3, we can rewrite the expression as<br \/>\n(7x^2)^3-(2y)^3<\/p>\n<p>Carefully substituting 7x^2 for a and 2y for b, we arrive at<\/p>\n<p>343x^6-8y^3=(7x^2-2y)((7x^2)^2+(7x^2)(2y)+(2y)^2))<\/p>\n<p>Finally we simplify to<\/p>\n<p>(7x^2-2y)(49x^4+14x^2y+4y^2)<\/p>\n<p>The key with using these formulas is knowing how to rewrite your own expression so the proper substitution can be made.<\/p>\n<p>Cheers,<\/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>The math tutor continues with factoring cubes. \u00a0Tutoring calculus, this formula is another standby. Let&#8217;s turn to factoring x^3 &#8211; 64. Realizing that 64=4^3, you actually are facing x^3-4^3 You need the formula a^3 &#8211; b^3=(a-b)(a^2 + ab + b^2) &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-factoring-difference-of-cubes\/\"> <span class=\"screen-reader-text\">Math:  factoring difference 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":[64,35],"class_list":["post-3411","post","type-post","status-publish","format-standard","hentry","category-math","tag-difference-of-cubes","tag-factoring"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/3411","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=3411"}],"version-history":[{"count":23,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/3411\/revisions"}],"predecessor-version":[{"id":23512,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/3411\/revisions\/23512"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=3411"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=3411"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=3411"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}