因式分解(x+y)*3+(z-x)*3-(y+z)*3

(x+y)*3+(z-x)*3-(y+z)*3
你是在用 * 表示 乘方 吧。这里一般用 ^ 表示 乘方，而用*表示 相乘。以后出题目请入乡随俗吧。
(x+y)^3 + (z-x)^3 - (y+z)^3 =
x^3 + 3x^2y + 3xy^2 + y^3 + z^3 -3z^2x + 3zx^2 - x^3 - y^3 - 3y^2z -3yz^2 - z^3
=3x^2y + 3xy^2 - 3z^2x + 3zx^2 -3y^2z - 3yz^2
=3x^2(y+z) + 3x(y^2-z^2) -3yz(y+z)
=3x^2(y+z) + 3x(y-z)(y+z) -3yz(y+z)
=3(y+z)(x^2 + xy - xz - yz)
=3(y+z)[x(x+y) - z(x+y)]
=3(y+z)(x+y)(x-z)

(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).