Solve xy^4-y^3+xy^2-y=

$$x y ^ { 4 } - y ^ { 3 } + x y ^ { 2 } - y =$$

Factor

$$y\left(y^{2}+1\right)\left(xy-1\right)$$

Solution Steps

Factor out y.

$$y\left(xy^{3}-y^{2}+xy-1\right)$$

Consider xy^{3}-y^{2}+xy-1. Do the grouping xy^{3}-y^{2}+xy-1=\left(xy^{3}-y^{2}\right)+\left(xy-1\right), and factor out y^{2} in xy^{3}-y^{2}.

$$y^{2}\left(xy-1\right)+xy-1$$

Factor out common term xy-1 by using distributive property.

$$\left(xy-1\right)\left(y^{2}+1\right)$$

Rewrite the complete factored expression. Polynomial y^{2}+1 is not factored since it does not have any rational roots.

$$y\left(xy-1\right)\left(y^{2}+1\right)$$

Evaluate

$$y\left(y^{2}+1\right)\left(xy-1\right)$$