Question

[Trần Long]

 

Answer 1

[HT.Phong (9A5)]

\(x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\\ =x^2y-x^2z+y^2z-xy^2+xz^2-yz^2\\ =\left(x^2y-x^2z\right)+\left(y^2z-yz^2\right)-\left(xy^2-xz^2\right)\\ =x^2\left(y-z\right)+yz\left(y-z\right)-x\left(y^2-z^2\right)\\ =x^2\left(y-z\right)+yz\left(y-z\right)-x\left(y+z\right)\left(y-z\right)\\ =\left(y-z\right)\left[x^2+yz-x\left(y+z\right)\right]\\ =\left(y-z\right)\left(x^2+yz-xy-xz\right)\\ =\left(y-z\right)\left[x\left(x-y\right)-z\left(x-y\right)\right]\\ =\left(y-z\right)\left(x-z\right)\left(x-y\right)\)