作业帮(x+y+z)(-x+y+z)(x-y+z)(x+y-z)等于什么?
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/02 08:37:38
(x+y+z)(-x+y+z)(x-y+z)(x+y-z)等于什么?
(x+y+z)(-x+y+z)(x-y+z)(x+y-z)等于什么?
(x+y+z)(-x+y+z)(x-y+z)(x+y-z)等于什么?
题目应为:
（x+y-z)(x-y+z)-(x+y+z)(x-y-z)
=[x+(y-z)][x-(y-z)]-[x+(y+z)][x-(y+z)]
=x^2-(y-z)^2-[x^2-(y+z)^2]
=(y+z)^2-(y-z)^2
=(y+z+y-z)(y+z-y+z)
=2y*2z
=4yz
(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]=4(x^2)(y^2)-(x*x+y*y-z*z)^2
反正就是反复利用平方差公式,还可以继续化简，希望对你有所帮助
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