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