Generalize the pattern for the division of (x^n)-(y^n) by x-y

Answer 1

set up a long algebraic divsion , hard to show in this format
I hope you know how to perform that
I got

x^n - y^n = (x-y)(x^(n-1) + yx^(n-2) + y^2 x^(n-3) + ... + y^(n-1) )