Question

1. Phân tích thành nhân tử:

xy(x + y) + yz(y + z) + xz(x+z) + 2xyz

Answer 1

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

\(=x^2y+xy^2+y^2z+yz^2+xz\left(x+z\right)+2xyz\)

\(=\left(x^2y+xyz\right)+\left(xy^2+y^2z\right)+\text{(}yz^2+xyz\text{)}+xz\left(x+z\right)\)

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

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

\(=\left(x+z\right)\text{[}y\left(x+y\right)+z\left(x+y\right)\text{]}\)

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