(x+y+z)(-x+y+z)(x-y+z)(x+y-z)等于什么？（过程）
答案:2 悬赏:80
解决时间 2021-03-08 03:03
- 提问者网友：乏味沐染
- 2021-03-07 10:17
(x+y+z)(-x+y+z)(x-y+z)(x+y-z)等于什么？（过程）
最佳答案
- 二级知识专家网友：劳资的心禁止访问
- 2021-03-07 11:20
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)]-[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
全部回答
- 1楼网友：颜值超标
- 2021-03-07 11:36
(x+y+z)(-x+y+z)(x-y+z)(x+y-z)
=[x+（y+z）] [(y+z）-x] [x-（y-z)] [x+（y-z)]
=[(y+z）²-x²][x²-（y-z）²]
=(y+z）²x²-(y+z）²（y-z）²-x⁴+x²（y-z）²
=x²[(y+z）²+（y-z）²]-（y²-z²）²-x⁴
=x²（2y²+2z²）-y⁴+2y²z²-z⁴-x⁴
=-x⁴-y⁴-z⁴+2x²y²+2x²z²+2y²z²
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