Question

PHÂN TÍCH ĐA THỨC THÀNH NHÂN TỬ : `x( y^2 - z^2 ) + y ( z^2 -x^2 ) + ( x^2 - y^2)`

Answer 1

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

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

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

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

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

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