分解因式(x^2+y^2-z^2)^2-4x^2y^2

(x^2+y^2-z^2)^2-4x^2y^2
利用平方差公式
(x^2+y^2-z^2)^2-4x^2y^2
=[(x^2+y^2-z^2)+2xy][(x^2+y^2-z^2)-2xy]
=[x^2+y^2+2xy-z^2][x^2-2xy+y^2-z^2]
=[(x+y)^2-z^2][(x-y)^2-z^2]
=(x+y+z)(x+y-z)(x-y+z)(x-y-z)

原式＝（x^2+y^2-z^2-2xy)(x^2+y^2-z^2+2xy)
=[(x-y)^2-z^2][(x+y)^2-z^2]
=(x-y-z)(x-y+z)(x+y-z)(x+y+z)

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

再往下就不能分解了