如何因式分解 xyz(x^3+y^3+z^3)-x^3y^3-y^3z^3-z^3x^3

题目

如何因式分解 xyz(x^3+y^3+z^3)-x^3y^3-y^3z^3-z^3x^3

答案

xyz(x³+y³+z³)-x³y³-y³z³-z³x³
=x^4yz+xyz(y³+z³)-y³z³-x³(y³+z³)
=yz(x^4-y²z²)+x(yz-x²)(y³+z³)
=yz(x²+yz)(x²-yz)-x(x²-yz)(y³+z³)
=(x²-yz)(x²yz+y²z²-xy³-xz³)
=(x²-yz)[y²(z²-xy)-xz(z²-xy)]
=(x²-yz)(y²-xz)(z²-xy)
乐意为您解答!