分类：教育/科学-升学入学-中考
问题：因式分解(yz^4+zx^4+xy^4)
因式分解
(yz^4+zx^4+xy^4)-(zy^4+xz^4+yx^4)
回答：(yz^4+zx^4+xy^4)-(zy^4+xz^4+yx^4)
=yz(z^3-y^3)+zx(x^3-z^3)+xy(y^3-x^3)
=yz(z-y)(z^2+yz+y^2)+zx(x-z)(x^2+zx+z^2)+xy(y-x)(y^2+xy+x^2)
=yz(z-y)(z^2+yz+y^2)+zx(x-y)(x^2+zx+z^2)+zx(y-z)(x^2+zx+z^2)+xy(y-x)(y^2+xy+x^2)
=z(z-y)[y(z^2+yz+y^2)-x(x^2+zx+z^2)]+x(y-x)[y(y^2+xy+x^2)-z(x^2+zx+z^2)
=z(z-y)(y-x)[z^2+z(y+x)+y^2+xy+x^2]-x(y-x)*(z-y)[x^2+x(y+z)+y^2+yz+z^2]
=(z-y)(y-x)(z-x)[z^2+zx+x^2+yz+x(y+z)+y^2-zx]
=(z-y)(y-x)(z-x)[x^2+y^2+z^2+yz+xy+zx]