题目

因式分解(x+y)*3+(z-x)*3-(y+z)*3

提问时间：2021-01-09

答案

(x+y)*3+(z-x)*3-(y+z)*3
=(x+y)*3+[(z-x)-(y+z)][(z-x)^2+(z-x)(y+z)+(y+z)^2]
=(x+y)*3+[-(x+y)](z^2-2xz+x^2+yz+z^2-xy-xz+y^2+2yz+z^2)
=(x+y)*3-(x+y)(3z^2+x^2+y^2-3xz+3yz-xy)
=(x+y)[(x+y)^2-(3z^2+x^2+y^2-3xz+3yz-xy)]
=(x+y)(x^2+2xy+y^2-3z^2-x^2-y^2+3xz-3yz+xy)
=(x+y)(3xy+3xz-3yz-3z^2)
=3(x+y)[x(y+z)-z(y+z)]
=3(x+y)(y+z)(x-z).