13问答网 > 因式分解:x^2(y+z)+y^2(z+x)+z^2(x+y)-(x^3+y^3+z^3)-2xyz

因式分解:x^2(y+z)+y^2(z+x)+z^2(x+y)-(x^3+y^3+z^3)-2xyz

运用到"轮换多项式"的一些解题方法.谢谢

2025-02-26 06:57:27

推荐回答（1个）

回答1：

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)