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

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/08/27 08:26:26

(x+y-z)²+(x+y-z)(x+y+z)-2z(x-y)
=[(x+y)-z]²+[(x+y)-z][(x+y)+z]-2z(x-y)
=(x+y)²-2z(x+y)+z²+(x+y)²-z²-2z(x-y)
=-2z[(x+y)+(x-y)]
=-2z(2x)
=-4xz

应该是式子错了!没有答案!

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再问：对不起我打错了呢。。原式是若x+y=6,xy=-8,求代数式(x-y+z)^2+(x+y-z)(x+y+z)-2·z(x-y)
再答： (x-y+z)²+(x+y-z)(x+y+z)-2z(x-y) =[(x-y)-z]²+[(x+y)-z][(x+y)+z]-2z(x-y) =(x-y)²-2z(x-y)+z²+(x+y)²-z²-2z(x-y) =(x-y)²+(x+y)² =(x²-2xy+y²)+(x²+2xy+y²) =2x²+2y² =2(x²+y²) =2[(x+y)²-2xy] =2×[6²-2×(-8)] =2×(36+16) =2×52 =104

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