Question

Phân tích đa thức thành nhân tử ;

\(x^2+x^2-x^2y^2+xy-x-y\)

Answer 1

\(x^2+y^2-x^2y^2+xy-x-y\)

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

\(=x^2\left(1-y^2\right)+y\left(y-1\right)+x\left(y-1\right)\)

\(=x^2\left(1-y\right)\left(1+y\right)+y\left(y-1\right)+x\left(y-1\right)\)

\(=x^2\left(1-y\right)\left(1+y\right)-y\left(1-y\right)-x\left(1-y\right)\)

\(=\left(1-y\right)\left(x^2+x^2y-x-y\right)\)

\(=\left(1-y\right)\left[\left(x^2y-y\right)+\left(x^2-x\right)\right]\)

\(=\left(1-y\right)\left[y\left(x-1\right)\left(x+1\right)+x\left(x-1\right)\right]\)

\(=\left(1-y\right)\left(x-1\right)\left(xy+y+x\right)\)