分解因式(x+y+z)(x-y+z)+(y-x+z)(y-x-z)过程。
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解决时间 2021-03-25 23:59
- 提问者网友：末路
- 2021-03-25 03:07
分解因式(x+y+z)(x-y+z)+(y-x+z)(y-x-z)过程。
最佳答案
- 五星知识达人网友：梦中风几里
- 2021-03-25 04:22
解：原式=(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-y-z)(x-y+z)
=2x(x-y+z)
望采纳!!!!!!!!!!!!!!!!!!!!
=[(x+y+z)+(x-y-z)](x-y+z)
=(x+y+z+x-y-z)(x-y+z)
=2x(x-y+z)
望采纳!!!!!!!!!!!!!!!!!!!!
全部回答
- 1楼网友：动情书生
- 2021-03-25 07:45
健康长寿网！
- 2楼网友：刀戟声无边
- 2021-03-25 07:03
=（x+z）（x+z）-y*y+(y-x)(y-x)-z*z
=x*x+2x*z+z*z-y*y+y*y-2x*y+x*x-z*z
=2x*（x+z-y)
=x*x+2x*z+z*z-y*y+y*y-2x*y+x*x-z*z
=2x*（x+z-y)
- 3楼网友：十年萤火照君眠
- 2021-03-25 05:57
(x+y+z)(x-y+z)+(y-x+z)(y-x-z)
=(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-y-z)(x-y+z)
=2x(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+y+z+x-y-z)(x-y+z)
=2x(x-y+z)
- 4楼网友：忘川信使
- 2021-03-25 05:40
(x+y+z)(x-y+z)+(y-x+z)(y-x-z)
=(x+z+y)(x+z-y)+(z-x+y)(-z-x+y)
=(x+z)^2-y^2 +[z-(x-y)][-z-(x-y)]
= (x+z)^2 - y^2 -[z-(x-y)][z+(x-y)]
= (x+z)^2 - y^2 - z^2 +(x-y)^2
= x^2+2xz+z^2-y^2-z^2+x^2-2xy+y^2
= 2x^2+2xz-2xy
= 2x(x+z-y)
= 2x(x-y+z)
......................
........................
=(x+z+y)(x+z-y)+(z-x+y)(-z-x+y)
=(x+z)^2-y^2 +[z-(x-y)][-z-(x-y)]
= (x+z)^2 - y^2 -[z-(x-y)][z+(x-y)]
= (x+z)^2 - y^2 - z^2 +(x-y)^2
= x^2+2xz+z^2-y^2-z^2+x^2-2xy+y^2
= 2x^2+2xz-2xy
= 2x(x+z-y)
= 2x(x-y+z)
......................
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