Phân tích đa thức thành nhân tử: x^2 +y^2 -x^2 y^2 +xy -x -y

* Hướng dẫn giải

$$\begin{gathered} x^2+y^2-x^2{y}^2+xy-x-y \\ =\left(x^2-x\right)+\left(y^2-x^2{y}^2\right)+\left(xy-y\right) \end{gathered}$$

$$\begin{gathered} \begin{array}{l}=x\left(x-1\right)+y^2\left(1-x^2\right)+y\left(x-1\right)\\ =x\left(x-1\right)+y^2\left(x-1\right)\left(x+1\right)+y\left(x-1\right)\end{array} \\ \begin{array}{l}=\left(x-1\right)\left[x-y^2\left(x+1\right)+y\right]\\ =\left(x-1\right)\left[\left(x-y^{2}x\right)-\left(y^2-y\right)\right]\\ =\left(x-1\right)\left[x\left(1-y^2\right)-y\left(y-1\right)\right]\\ =\left(x-1\right)\left[x\left(1-y\right)\left(1+y\right)+y\left(1-y\right)\right]\\ =\left(x-1\right)\left(1-y\right)\left(x+xy+y\right)\end{array} \end{gathered}$$