(x-1)x^3y^3+(1-x)^3z^3,因式分解

(x-1)x^3y^3+(1-x)^3z^3,因式分解
(x-1)x^3y^3+(1-x)^3z^3,因式分解

(x-1)x^3y^3+(1-x)^3z^3,因式分解
(x-1)^3y^3+(1-x)^3z^3
=(x-1)^3y^3-(x-1)^3z^3
=(x-1)^3(y^3-z^3)
=(x-1)^3(y-z)(y^2+yz+z^2)
(x-1)x^3y^3+(1-x)x^3z^3
=(x-1)x^3y^3-(x-1)x^3z^3
=(x-1)x^3(y^3-z^3)
=(x-1)x^3(y-z)(y^2+yz+z^2)
两个总有一个是对的.

不要被三次方吓到了；就是提取公因式，然后三次方化简就完了
(x-1)x^3y^3+(1-x)x^3z^3
=(x-1)x^3y^3-(x-1)x^3z^3
=(x-1)x^3(y^3-z^3)
=(x-1)x^3(y-z)(y^2+yz+z^2)

提取公因式,最后一步用到公式a^3+b^3=(a+b)(a^2-ab+b^2)
(x-1)x^3y^3+(1-x)x^3z^3
=(x-1)x^3y^3-(x-1)x^3z^3
=(x-1)x^3(y^3-z^3)
=(x-1)x^3(y-z)(y^2+yz+z^2)