Question

Phân tích đa thức thành nhân tử : \(x\left(y+z\right)^2+y\left(x+z\right)^2+z\left(x+y\right)^2-4xyz\)

Answer 1

Có \(x\left(y+z\right)^2+y\left(x+z\right)^2+z\left(x+y\right)^2-4xyz\)

\(=xy^2+2xyz+xz^2+yx^2+2xyz+yz^2+zx^2+2xyz+zy^2-4xyz\)

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

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

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

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

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

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

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

Chúc bạn học tốt!