Question

x^3n -y^3n is divisible by x-y

Answer 1

x^3n - y^3n = n(x^3 - y^3)

x^3 - y^3 = (x-y)(x^2 +xy + y^2)

(n)(x-y)(x^2 + xy + y^2)/(x-y) = (n)(x^2 + xy + y^2)

That is the simplest answer, but if you want to expand it you can multiply the two terms and get:

x^2n + xyn + y^2n

Therefore, x^3n - y^3n is divisible by x-y.