Solve x^{2}-xy+xz-xy^{2}z^{2}+y^3z^2-y^2z^3

$$x ^ { 2 } - x y + x z - x y ^ { 2 } z ^ { 2 } + y ^ { 3 } z ^ { 2 } - y ^ { 2 } z ^ { 3 }$$

Factor

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

Solution Steps

Do the grouping x^{2}-xy+xz-xy^{2}z^{2}+y^{3}z^{2}-y^{2}z^{3}=\left(x^{2}-xy+xz\right)+\left(-xy^{2}z^{2}+y^{3}z^{2}-y^{2}z^{3}\right), and factor out x in the first and -y^{2}z^{2} in the second group.

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

Factor out common term x-y+z by using distributive property.

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

Evaluate

$$\left(x-y+z\right)\left(x-\left(yz\right)^{2}\right)$$