Question

Phân tích đa thức thành nhân tử:

\(xy\left(x-y\right)-xz\left(x+z\right)+yz\left(2x-y+z\right)\)

GIÚP MIK VỚI !!!!!!!!!!!!

Answer 1

\(xy\left(x-y\right)-xz\left(x+z\right)+yz\left(2x-y+z\right)\)

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

\(=xy\left(x-y\right)-xz\left(x+z\right)+yz\left(x-y\right)+yz\left(x+z\right)\)

\(=\left(x-y\right)\left(xy+yz\right)+\left(x+z\right)\left(yz-xz\right)\)

\(=y\left(x-y\right)\left(x+z\right)-z\left(x+z\right)\left(x-y\right)\)

\(=\left(x-y\right)\left(x+z\right)\left(y-z\right)\)