作业帮因式分解(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/05/01 11:45:11
因式分解(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3
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(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3
=((x+y+z)^3-(y+z-x)^3)-((z+x-y)^3+(x+y-z)^3)
=(x+y+z-y-z+x)((x+y+z)^2+(x+y+z)(y+z-x)+(y+z-x)^2)-
(z+x-y+x-z+y)((z+x-y)^2-(z+x-y)(x+y-z)+(x+y-z)^2)
=2x((x+y+z)^2+(x+y+z)(y+z-x)+(y+z-x)^2-(z+x-y)^2+(z+x-y)(x+y-z)-(x+y-z)^2)
=2x((x+y+z+z+x-y)(x+y+z-z-x+y)+(y+z-x+x+y-z)(y+z-x-x-y+z)+(x+y+z)(y+z-x)+(z+x-y)(x+y-z))
=2x(12yz)
=24xyz
=((x+y+z)^3-(y+z-x)^3)-((z+x-y)^3+(x+y-z)^3)
=(x+y+z-y-z+x)((x+y+z)^2+(x+y+z)(y+z-x)+(y+z-x)^2)-
(z+x-y+x-z+y)((z+x-y)^2-(z+x-y)(x+y-z)+(x+y-z)^2)
=2x((x+y+z)^2+(x+y+z)(y+z-x)+(y+z-x)^2-(z+x-y)^2+(z+x-y)(x+y-z)-(x+y-z)^2)
=2x((x+y+z+z+x-y)(x+y+z-z-x+y)+(y+z-x+x+y-z)(y+z-x-x-y+z)+(x+y+z)(y+z-x)+(z+x-y)(x+y-z))
=2x(12yz)
=24xyz
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