Lutasin ang xy^4-y^3+xy^2-y=

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

I-factor

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

Mga Hakbang ng Solution

I-factor out ang y.

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

Isaalang-alang ang xy^{3}-y^{2}+xy-1. Gawin ang grouping na xy^{3}-y^{2}+xy-1=\left(xy^{3}-y^{2}\right)+\left(xy-1\right), at i-factor out ang y^{2} sa xy^{3}-y^{2}.

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

I-factor out ang common term na xy-1 gamit ang distributive property.

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

I-rewrite ang kumpletong naka-factor na expression. Ang polynomial y^{2}+1 ay hindi naka-factor dahil wala itong anumang rational root.

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

I-evaluate

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