x^8 - y^8 = (x - y)(x + y)(x^2 + y^2)(x^4 + y^4) x^8 - y^8 = (x^2 - y^2)(x^2 + y^2)(x^4 + y^4) x^8 - y^8 = (x^4 - y^4)(x^4 + y^4) x^8 - y^8 = x^8 - y^8