How do you divide $(x^5 + y^5) /(x + y)$ ?

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Answer 1 · 2016-03-07T23:16:02

For $n$ odd integer the following identity holds

$x^n + y^n = (x + y)(x^{n-1} - x^{n-2}y + \cdots - xy^{n-2} + y^{n-1} )$

or

$[x^n + y^n]/[x+y]=(x^{n-1} - x^{n-2}y + \cdots - xy^{n-2} + y^{n-1} )$

Hence for our case we have that

$[x^5+y^5]/[x+y]=x^4-x^3 y+x^2 y^2-x y^3+y^4$

How do you divide (x^5 + y^5) /(x + y) (x^5 + y^5) /(x + y)?