Question

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

Answer 1

It's very simply
(x-y)(x^3+x^2y+xy^2+y^3= (x-y)(x^2(x+y) +y^2(x+y))=(x-y)(x+y)(x^2+y^2)=(x^2-y^2)(x^2+y^2)=x^4-y^4
Good luck