Question

Phân tích đa thức thành nhân tử:

xy(x+y) - yz(z+y)+xz(x-z)

Answer 1

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

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

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

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

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

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