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

$$\quad x ^ { 3 } - x y ^ { 2 } - y ^ { 3 } + x ^ { 2 } y$$

Factor

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

Solution Steps

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

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

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

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

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.

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

Evaluate

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