化简(x+y+z)^2-(-x+y+z)^2+(x-y+z)^2-(x+y-z)^2

问题补充：

化简(x+y+z)^2-(-x+y+z)^2+(x-y+z)^2-(x+y-z)^2

答案：

利用A^2-B^2=(A+B)(A-B)即可.

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

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

={[(x+y+z)+(-x+y+z)]*[(x+y+z)-(-x+y+z)]}+{[(x-y+z)+(x+y-z)]*[(x-y+z)-(x+y-z)]}

=[(2y+2z)*2x]+[2x*(-2y)]

=4xy+4xz+(-4xy)

=4xz