因式分解:x^2(y+z)+y^2(z+x)+z^2(x+y)-(x^3+y^3+z^3)-2xyz
答案:1 悬赏:60 手机版
解决时间 2021-02-12 19:33
- 提问者网友:戎马万世
- 2021-02-12 08:35
因式分解:x^2(y+z)+y^2(z+x)+z^2(x+y)-(x^3+y^3+z^3)-2xyz
最佳答案
- 五星知识达人网友:动情书生
- 2021-02-12 09:16
x^2(y+z)+y^2(z+x)+z^2(x+y)-(x^3+y^3+z^3)-2xyz
=x^2(y+z)+y^2*z+y^2*x+z^2*x+z^2*y-x^3-y^3-z^3-2xyz
=x^2(y+z-x)+x(y^2+z^2-2yz)+(y^2*z+z^2*y-y^3-z^3)
=x^2(y+z-x)+x(y-z)^2+[y^2(z-y)-z^2(z-y)]
=x^2(y+z-x)+x(y-z)^2+(y+z)(y-z)(z-y)
=x^2(y+z-x)+x(y-z)^2-(y+z)(y-z)^2
=x^2(y+z-x)+(y-z)^2(x-y-z)
=(x-y-z)(z-y-x)(z-y+x)
=x^2(y+z)+y^2*z+y^2*x+z^2*x+z^2*y-x^3-y^3-z^3-2xyz
=x^2(y+z-x)+x(y^2+z^2-2yz)+(y^2*z+z^2*y-y^3-z^3)
=x^2(y+z-x)+x(y-z)^2+[y^2(z-y)-z^2(z-y)]
=x^2(y+z-x)+x(y-z)^2+(y+z)(y-z)(z-y)
=x^2(y+z-x)+x(y-z)^2-(y+z)(y-z)^2
=x^2(y+z-x)+(y-z)^2(x-y-z)
=(x-y-z)(z-y-x)(z-y+x)
我要举报
如以上问答信息为低俗、色情、不良、暴力、侵权、涉及违法等信息,可以点下面链接进行举报!
大家都在看
推荐资讯