Usually we will expand powers just by expanding it using normal multiplication or using the following formulae.<\/p>\n
(a+b)^2 = a^2 + 2ab + b^2<\/strong> Fine. We can use these formulae when the power is either 2 or 3. But, Is there any formula for the expansion of (a+b)^4<\/strong>? We may say we can expand it. Yes. We can expand though it is a bit difficult.<\/p>\n But what if the powers are big numbers like 5,6,7,8\u2026.?<\/p>\n We have a solution for this called \u201cBinomial theorem\u201d which is used for the expansion of binomials with different powers (higher powers even). Example 1:<\/strong><\/p>\n <\/strong>Expand (x+y)^5<\/strong> using binomial theorem.<\/p>\n Solution:<\/strong><\/em><\/span><\/p>\n <\/strong>Substituting a=x, b=y and n=5 in the expansion of binomial theorem, Example 2:<\/strong><\/p>\n Expand (x-y)^5<\/strong> using binomial theorem.<\/p>\n Solution:<\/strong><\/em><\/span><\/p>\n Substituting a=x, b=y<\/strong> and n=5<\/strong> in the expansion of binomial theorem, SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Palm Desert visit: Tutoring in Palm Desert. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":" Usually we will expand powers just by expanding it using normal multiplication or using the following formulae. (a+b)^2 = a^2 + 2ab + b^2 (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 Fine. We can use these formulae when the power is either 2 or 3. But, Is there any formula for the expansion […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[879,991,1920,2217],"class_list":["post-3059","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-how-to-expand-binomial-theorem","tag-is-there-a-shortcut-for-expanding-formulae","tag-using-mathematical-expansion","tag-what-is-binomial-theorem"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/3059","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=3059"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/3059\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=3059"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=3059"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=3059"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3<\/strong><\/p>\n
\nBinomial theorem is defined as follows.
\n(a+b)^n = nC0 a^n + nC1 a^(n-1) b + nC2 a^(n-2) b^2 + \u2026 + nCn b^n<\/strong>
\n (a-b)^n = nC0 a^n – nC1 a^(n-1) b + nC2 a^(n-2) b^2 – \u2026 + (-1)^n nCn b^n<\/strong>
\nThe process of expansions using Binomial theorem is explained through the following examples.
\n<\/strong><\/p>\n
\n(x+y) 5 = 5C0 x^5 + 5C1 x^4 y + 5C2 x^3 y^2 + 5C3 x^2 y^3 + 5C4 x y^4 + 5C5 y^5<\/strong>
\n = x^5 + 5x^4 y + 10 x^3 y^2 + 10 x^2 y^3 + 5 x y^4 + y^5<\/strong>
\n(Here, 5C0=1, 5C1=5, 5C2=10, 5C3=10, 5C4=5, 5C5=1<\/strong>).
\n<\/strong><\/p>\n
\n(x-y) 5 = 5C0 x^5 – 5C1 x^4 y + 5C2 x^3 y^2 – 5C3 x^2 y^3 + 5C4 x y^4 – 5C5 y^5<\/strong>
\n = x^5 – 5x^4 y + 10 x^3 y^2 – 10 x^2 y^3 + 5 x y^4 – y^5<\/strong>
\n(Here, 5C0=1, 5C1=5, 5C2=10, 5C3=10, 5C4=5, 5C5=1<\/strong>).<\/p>\n