如何化简(x+y+z)(x+y-z)(x-y+z)(-x+y+z)
问题描述：
如何化简(x+y+z)(x+y-z)(x-y+z)(-x+y+z)
答
应用平方差公式
a^2-b^2=(a+b)(a-b)
(x+y+z)(x+y-z)(x-y+z)(-x+y+z)
=[(x+y)^2-z^2][z^2-(x-y)^2]
=-z^4+[(x+y)^2+(x-y)^2]z^2-(x+y)^2(x-y)^2
=-z^4+2(x^2+y^2)z^2-(x^2-y^2)^2
这算是化简了