Solve x^3-xy^2-x^2z+y^2z

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

Factor

$$\left(x-y\right)\left(x-z\right)\left(x+y\right)$$

Solution Steps

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

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

Factor out common term x^{2}-y^{2} by using distributive property.

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

Consider x^{2}-y^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-y\right)\left(x+y\right)$$

Rewrite the complete factored expression.

$$\left(x-y\right)\left(x+y\right)\left(x-z\right)$$

Evaluate

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