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 March 30th, 2014, 05:33 AM #1 Senior Member   Joined: Nov 2013 Posts: 137 Thanks: 1 Binomials I was verifying that $\\x^2-y^2=(x-y)(x+y) \\x^3-y^3=(x-y)(x^2+xy+y^2)$ and I realized that can there is a formulation more general like the theorem binomial... my question is: exist a general theorem for sum or difference of terms^n ?
 March 30th, 2014, 06:23 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,966 Thanks: 2216 $x^n\,-\,y^n\,=\,(x\,-\,y)\sum_{r=1}^nx^{n-r}y^{r-1}$ If n is odd, replace y with -y to get the corresponding "sum" formula. Thanks from agentredlum
 March 30th, 2014, 07:08 AM #3 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Yes, of course there is a general form for these. One involves $x^n - y^n$ (the even and odd case) and the other $x^n + y^n$ (only the odd case). The latter is easily derived from a complex bit of trig. Thanks from agentredlum

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