若x-y=6,xy=-8,求代数式(x+y+z)²+(x-y-z)(x-y+z)-2·z(x+y)的值

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若x-y=6,xy=-8,求代数式(x+y+z)²+(x-y-z)(x-y+z)-2·z(x+y)的值

若x-y=6,xy=-8,求代数式(x+y+z)²+(x-y-z)(x-y+z)-2·z(x+y)的值
若x-y=6,xy=-8,求代数式(x+y+z)²+(x-y-z)(x-y+z)-2·z(x+y)的值

若x-y=6,xy=-8,求代数式(x+y+z)²+(x-y-z)(x-y+z)-2·z(x+y)的值
(x+y+z)²+(x-y-z)(x-y+z)-2·z(x+y)
=(x+y)²+2z(x+y)+z²+(x-y)²-z²-2z(x+y)
=(x+y)²+(x-y)²
=(x-y)²+4xy+6²
=6²-4x8+36
=72-32
=40
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