（x+y+z）³+（3x-2y-3z）³-（4x-y-2z）³分解因式
答案:4 悬赏:0
解决时间 2021-01-18 22:50
- 提问者网友：绫月
- 2021-01-18 01:02
（x+y+z）³+（3x-2y-3z）³-（4x-y-2z）³分解因式
最佳答案
- 二级知识专家网友：躲不过心动
- 2021-01-18 01:42
(x+y+z)3+(3x-2y-3z)3-(4x-y-2z)3
=(4x-y-2z)[(x+y+z)^2-2(x+y+z)(3x-2y-3z)+(3x-2y-3z)^2]-(4x-y-2z)3
=(4x-y-2z)[(x+y+z)^2-2(x+y+z)(3x-2y-3z)+(3x-2y-3z)^2-(4x-y-2z)^2]
=(4x-y-2z)[(x+y+z)((x+y+z)-(3x-2y-3z))+((3x-2y-3z)-(4x-y-2z))((3x-2y-3z)+(4x-y-2z))]
=(4x-y-2z)[(x+y+z)(-2x+3y+4z)+(-x-y-z)(7x-3y-5z)]
=(4x-y-2z)(x+y+z)[(-2x+3y+4z)-(7x-3y-5z)]
=(4x-y-2z)(x+y+z)(-9x+6y+9z)
=3(4x-y-2z)(x+y+z)(-3x+2y+3z)
=(4x-y-2z)[(x+y+z)^2-2(x+y+z)(3x-2y-3z)+(3x-2y-3z)^2]-(4x-y-2z)3
=(4x-y-2z)[(x+y+z)^2-2(x+y+z)(3x-2y-3z)+(3x-2y-3z)^2-(4x-y-2z)^2]
=(4x-y-2z)[(x+y+z)((x+y+z)-(3x-2y-3z))+((3x-2y-3z)-(4x-y-2z))((3x-2y-3z)+(4x-y-2z))]
=(4x-y-2z)[(x+y+z)(-2x+3y+4z)+(-x-y-z)(7x-3y-5z)]
=(4x-y-2z)(x+y+z)[(-2x+3y+4z)-(7x-3y-5z)]
=(4x-y-2z)(x+y+z)(-9x+6y+9z)
=3(4x-y-2z)(x+y+z)(-3x+2y+3z)
全部回答
- 1楼网友：duile
- 2021-01-18 05:05
- 2楼网友：走死在岁月里
- 2021-01-18 03:43
我暂时保留我的看法！
- 3楼网友：骨子里都是戏
- 2021-01-18 02:24
(x+y+z)³+(3x-2y-3z)³-(4x-y-2Z)³
=(x+y+z+3x-2y-3z)[(x+y+z)²-(x+y+z)(3x-2y-3z)+(3x-2y-3z)²]-(4x-y-2z)³
=(4x-y-2z)[(x+y+z)²-(x+y+z)(3x-2y-3z)+(3x-2y-3z)²-(4x-y-2z)²]
=-3(4x-y-2z)(x+y+z)(3x-2y-3z)
=(x+y+z+3x-2y-3z)[(x+y+z)²-(x+y+z)(3x-2y-3z)+(3x-2y-3z)²]-(4x-y-2z)³
=(4x-y-2z)[(x+y+z)²-(x+y+z)(3x-2y-3z)+(3x-2y-3z)²-(4x-y-2z)²]
=-3(4x-y-2z)(x+y+z)(3x-2y-3z)
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