Question

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

Answer 1

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