Factor x^4+x^3-4x^2-4x

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

Factor $x$ out of $x^{4} + x^{3} - 4 x^{2} - 4 x$ .

Factor $x$ out of $x^{4}$ .

$x \cdot x^{3} + x^{3} - 4 x^{2} - 4 x$

Factor $x$ out of $x^{3}$ .

$x \cdot x^{3} + x \cdot x^{2} - 4 x^{2} - 4 x$

Factor $x$ out of $- 4 x^{2}$ .

$x \cdot x^{3} + x \cdot x^{2} + x (- 4 x) - 4 x$

Factor $x$ out of $- 4 x$ .

$x \cdot x^{3} + x \cdot x^{2} + x (- 4 x) + x \cdot - 4$

Factor $x$ out of $x \cdot x^{3} + x \cdot x^{2}$ .

$x (x^{3} + x^{2}) + x (- 4 x) + x \cdot - 4$

Factor $x$ out of $x (x^{3} + x^{2}) + x (- 4 x)$ .

$x (x^{3} + x^{2} - 4 x) + x \cdot - 4$

Factor $x$ out of $x (x^{3} + x^{2} - 4 x) + x \cdot - 4$ .

$x (x^{3} + x^{2} - 4 x - 4)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$x ((x^{3} + x^{2}) - 4 x - 4)$

Factor out the greatest common factor (GCF) from each group.

$x (x^{2} (x + 1) - 4 (x + 1))$

Factor the polynomial by factoring out the greatest common factor, $x + 1$ .

$x ((x + 1) (x^{2} - 4))$

Rewrite $4$ as $2^{2}$ .

$x ((x + 1) (x^{2} - 2^{2}))$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

$x ((x + 1) ((x + 2) (x - 2)))$

Remove unnecessary parentheses.

$x ((x + 1) (x + 2) (x - 2))$

Remove unnecessary parentheses.

$x (x + 1) (x + 2) (x - 2)$