Question

分解因式(x^2+y^2)(x^2-xy+y^2)-2x^2y^2

要过程，如题，最后一项是2*x^2*y^2 (*代表乘号），谢谢，过程要详细一点

Answer 1

(x^2+y^2)(x^2-xy+y^2)-2x^2y^2
=[(x-y)^2+2xy][(x-y)^2+xy]-2x^2*y^2
=(x-y)^4+3xy(x-y)^2
=(x-y)^2*(x^2-2xy+y^2+3xy)
=(x-y)^2*(x^2+xy+y^2)

Answer 2

(x^2+y^2)(x^2-xy+y^2)-2x^2y^2
=x^4-x^3y-xy^3+2X^2y^2+y^4-2X^2y^2
=x^4-x^3y-xy^3+y^4
=(x^3-y^3)(x-y)
=(x-y)^2*(x^2+xy+y^2)