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