作业帮计算(x+y+z)(-x+y+z)(x-y+z)(x+y-z)
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/27 13:52:30
计算(x+y+z)(-x+y+z)(x-y+z)(x+y-z)
计算(x+y+z)(-x+y+z)(x-y+z)(x+y-z)
计算(x+y+z)(-x+y+z)(x-y+z)(x+y-z)
(x+y+z)(x-y+z)(x+y-z)(y+z-x)
=(((x+z)^2-y^2)(y^2-(x-z)^2))
=y^2((x+z)^2+(x-z)^2)-y^4-(x+z)^2(x-z)^2
=y^2(2x^2+2z^2)-y^4-(x^2-z^2)^2
=2x^2y^2+2y^2z^2-y^4-x^4-z^4+2x^2z^2
=2x^2y^2+2y^2z^2+2x^2z^2-x^4-y^4-z^4
x+y+z)(-x+y+z)(x-y+z)(x+y-z)
=[(x+y+z)(x+y-z)]*{[z+(x-y)][z-(x-y)]}
=[(x+y)^2-z^2][z^2-(x-y)^2]
=(x^2+2xy+y^2-z^2)[z^2-(x-y)^2]
=4*x^2*y^2-(x^2+y^2-z^2)^2
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