Question

Phân tích đa thức thành nhân tử : 

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

Answer 1

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

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

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

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

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