原式
=y(x^2-4xz+4z^2)+8xyz+x(y^2-4yz+4z^2)-2z(x+y)^2
=x^2y-4xyz+4yz^2+8xyz+xy^2-4xyz+4xz^2-2z(x+y)^2
=(x^2y+xy^2)+(4yz^2+4xz^2)-2z(x+y)^2
=xy(x+y)+4z^2(x+y)-2z(x+y)^2
=(x+y)[xy+4z^2-2z(x+y)]
=(x+y)(xy+4z^2-2xz-2yz)
=(x+y)[(xy-2xz)+(4z^2-2yz)]
=(x+y)[x(y-2z)-2z(y-2z)]
=(x+y)(y-2z)(x-2z).