Prove by mathematical induction that x^2n - y^2n has a factor of x+y.

Question

My answer is incomplete since i do not know what to do next. here it is:

i.) for n=1

x^2(1) - y^2(1) = x^2 - y^2
= (x+y)(x-y)

ii.) Assume that the proposition is true for all n=k, that is, x^2k - y^2k has a factor of x+y for all k¡Ý1.

iii.) n=k+1

x^2(k+1) - y^2(k+1)
=x^2k+2 - y^2k+2
=x^2k ¡ñ x^2 - y^2k ¡ñ y^2
=(tthis part I don't know)

I hope you can help me. Thanks!