(x+y+z)(-x+y+z)(x-y+z)(x+y-z)计算save me

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(x+y+z)(-x+y+z)(x-y+z)(x+y-z)计算save me

(x+y+z)(-x+y+z)(x-y+z)(x+y-z)计算save me
(x+y+z)(-x+y+z)(x-y+z)(x+y-z)计算
save me

(x+y+z)(-x+y+z)(x-y+z)(x+y-z)计算save me
原式=(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