Solve x^3+x^2y-4y-4x

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

Factor

$$\left(x-2\right)\left(x+2\right)\left(x+y\right)$$

Solution Steps

Do the grouping x^{3}+x^{2}y-4y-4x=\left(x^{3}+x^{2}y\right)+\left(-4y-4x\right), and factor out x^{2} in the first and -4 in the second group.

$$x^{2}\left(x+y\right)-4\left(x+y\right)$$

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

$$\left(x+y\right)\left(x^{2}-4\right)$$

Consider x^{2}-4. Rewrite x^{2}-4 as x^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2\right)\left(x+2\right)$$

Rewrite the complete factored expression.

$$\left(x-2\right)\left(x+2\right)\left(x+y\right)$$

Evaluate

$$\left(x+y\right)\left(x^{2}-4\right)$$