已知x+y+z=0,试求(x²-y²-z²)²-4y²z²的值
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已知x+y+z=0,试求(x²-y²-z²)²-4y²z²的值
已知x+y+z=0,试求(x²-y²-z²)²-4y²z²的值
已知x+y+z=0,试求(x²-y²-z²)²-4y²z²的值
(x²-y²-z²)²-4y²z²
=(x²-y²-z²)²-(2yz)²
=(x²-y²-z²-2yz)(x²-y²-z²+2yz)
=[x²-(y+z)²](x²-y²-z²+2yz)
=[x+y+z][x-(y+z)](x²-y²-z²+2yz)
=0*[x-(y+z)](x²-y²-z²+2yz)
=0
(x²-y²-z²)²-4y²z²=[x²-﹙y+z﹚²][x²-﹙y-z﹚²]=0
(x²-y²-z²)²-4y²z²
=(x²-y²-z²-2yz)(x²-y²-z²+2yz)
=(x²-(y+z)²)(x²-(y-z)²)
=(x-y-z)(x+y+z)(x-y+z)(x+y-z)
=0
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