(x+y+z)(-x+y+z)(x-y+z)(x+y-z)详 细

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(x+y+z)(-x+y+z)(x-y+z)(x+y-z)详 细
(x+y+z)(-x+y+z)(x-y+z)(x+y-z)详 细

(x+y+z)(-x+y+z)(x-y+z)(x+y-z)详 细
(x+y+z)(-x+y+z)(x-y+z)(x+y-z)
=[x+(y+z)] [(y+z)-x] [x-(y-z)] [x+(y-z)]
=[(y+z)²-x²][x²-(y-z)²]
=(y+z)²x²-(y+z)²(y-z)²-x⁴+x²(y-z)²
=x²[(y+z)²+(y-z)²]-(y²-z²)²-x⁴
=x²(2y²+2z²)-y⁴+2y²z²-z⁴-x⁴
=-x⁴-y⁴-z⁴+2x²y²+2x²z²+2y²z²