✨ Best Answer ✨
xy(x-y)+yz(y-z)+zx(z-x)
=xy(x-y)+z{y(y-z)+x(z-x)}
=xy(x-y)+z(y²-yz+zx-x²)
=xy(x-y)+z{z(x-y)-(x+y)(x-y)}
=(x-y){xy+z(z-(x+y))}
=(x-y){z²-(x+y)z+xy}
=(x-y)(z-x)(z-y)
=-(x-y)(y-z)(z-x)
✨ Best Answer ✨
xy(x-y)+yz(y-z)+zx(z-x)
=xy(x-y)+z{y(y-z)+x(z-x)}
=xy(x-y)+z(y²-yz+zx-x²)
=xy(x-y)+z{z(x-y)-(x+y)(x-y)}
=(x-y){xy+z(z-(x+y))}
=(x-y){z²-(x+y)z+xy}
=(x-y)(z-x)(z-y)
=-(x-y)(y-z)(z-x)
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