(x+y+z)(-x+y+z)(x-y+z)(x+y-z)等于什么

您好！

（x+y+z)(-x+y+z)(x-y+z)(x+y-z)

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

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

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

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

能明白吗？

(x+y+z)(x-y+z)(x+y-z)(y+z-x)
={[(x+z)^2-y^2][y^2-(x-z)^2]}
=y^2((x+z)^2+(x-z)^2)-y^4-(x+z)^2(x-z)^2
=y^2(2x^2+2z^2)-y^4-(x^2-z^2)^2
=2x^2y^2+2y^2z^2-y^4-x^4-z^4+2x^2z^2
=2x^2y^2+2y^2z^2+2x^2z^2-x^4-y^4-z^4

X+Y+Z
(x+y+z)(x-y+z)(x+y-z)(y+z-x)
=(((x+z)^2-y^2)(y^2-(x-z)^2))
=y^2((x+z)^2+(x-z)^2)-y^4-(x+z)^2(x-z)^2
=y^2(2x^2+2z^2)-y^4-(x^2-z^2)^2
=2x^2y^2+2y^2z^2-y^4-x^4-z^4+2x^2z^2
=2x^2y^2+2y^2z^2+2x^2z^2-x^4-y^4-z^4

你要问什么？展开吗？
-y^4-x^4-z^4+2*y^2*z^2+2*x^2*z^2+2*x^2*y^2