Question

How to solve this problem (x^n+y^n) divisible by (x+y)

Answer 1

`Use \\\\a^n + b^n = (a+b)(a^(n-1)b^0 - a^(n-2)b^1 + a^(n-3)b^2 - ... - a^1b^(n-2) + a^0b^(n-1)) \\--------------------------------\\\\(x^n+y^n)/(x+y)=((x+y)(x^(n-1)y^0-x^(n-2)y^1+x^(n-3)y^2-...-x^1y^(n-2)+x^0y^(n-1)))/(x+y)\\\\=\boxed{x^(n-1)-x^(n-2)y+x^(n-3)y^2-...-xy^(n-2)+y^(n-1)}`