x的立方(y-z)+y的立方(z-x)+z的立方( x-y)
=x³y－x³z＋y³z－xy³＋xz³－yz³
=（x³y－xy³)－(x³z－y³z)＋(xz³－yz³)
=xy(x²－y²)－z(x³－y³)＋z³(x－y)
=xy(x＋y)(x－y)－z(x－y)(x²＋xy＋y²)＋z³(x－y)
=(x－y)(x²y＋xy²－x²z－xyz－y²z＋z³)
=(x－y)[(x²y－x²z)＋(xy²－xyz)－(y²z－z³)]
=(x－y)[x²(y－z)＋xy(y－z)－z(y＋z)(y－z)]
=(x－y)(y－z)(x²＋xy－yz－z²)
=(x－y)(y－z)[(x²－z²)＋(xy－yz)]
=(x－y)(y－z)[(x＋z)(x－z)＋y(x－z)]
=(x－y)(y－z)(x－z)(x＋y＋z)