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March 30th, 2014, 05:33 AM   #1
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Binomials

I was verifying that



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 ?
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March 30th, 2014, 06:23 AM   #2
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If n is odd, replace y with -y to get the corresponding "sum" formula.
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March 30th, 2014, 07:08 AM   #3
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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.
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