Question

[Lan Chi Nguyen]

Phân tích đa thức thành nhân tử:

x^2( y - z )+y^2( z - x )+z^2( x - y)

Giải hộ mình nha!!!

Thanks you!!!

Answer 1

[Trà My]

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

\(=x^2\left(y-z\right)+y^2\left(z-y+y-x\right)+z^2\left(x-y\right)\)

\(=x^2\left(y-z\right)+y^2\left(z-y\right)+y^2\left(y-x\right)+z^2\left(x-y\right)\)

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

\(=\left(x^2-y^2\right)\left(y-z\right)+\left(y^2-z^2\right)\left(y-x\right)\)

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

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

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

Answer 2

[Lan Chi Nguyen]

Thanks you!!!