用因式分解表示 x^3+x^2y+x^2z+xyz

问题描述:

用因式分解表示 x^3+x^2y+x^2z+xyz


x^3+x^2y+x^2z+xyz
=x(x^2+xy+xz+yz)
=x[x(x+y)+z(x+y)]
=x(x+y)(x+z)

x^3+x^2y+x^2z+xyz
=x^2(x+y)+xz(x+y)
=(x^2+xz)(x+y)
=x(x+z)(x+y)