Algebra Examples

$2 x^{2} {(x + 1)}^{2} - 12 x (x + 1)$

Step 1

Factor $2 x (x + 1)$ out of $2 x^{2} {(x + 1)}^{2} - 12 x (x + 1)$ .

Tap for more steps...

Step 1.1

Factor $2 x (x + 1)$ out of $2 x^{2} {(x + 1)}^{2}$ .

$2 x (x + 1) (x (x + 1)) - 12 x (x + 1)$

Step 1.2

Factor $2 x (x + 1)$ out of $- 12 x (x + 1)$ .

$2 x (x + 1) (x (x + 1)) + 2 x (x + 1) (- 6)$

Step 1.3

Factor $2 x (x + 1)$ out of $2 x (x + 1) (x (x + 1)) + 2 x (x + 1) (- 6)$ .

$2 x (x + 1) (x (x + 1) - 6)$

Step 2

Apply the distributive property.

$2 x (x + 1) (x \cdot x + x \cdot 1 - 6)$

Step 3

Multiply $x$ by $x$ .

$2 x (x + 1) (x^{2} + x \cdot 1 - 6)$

Step 4

Multiply $x$ by $1$ .

$2 x (x + 1) (x^{2} + x - 6)$

Step 5

Factor.

Tap for more steps...

Step 5.1

Factor $x^{2} + x - 6$ using the AC method.

Tap for more steps...

Step 5.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $1$ .

$- 2, 3$

Step 5.1.2

Write the factored form using these integers.

$2 x (x + 1) ((x - 2) (x + 3))$

Step 5.2

Remove unnecessary parentheses.

$2 x (x + 1) (x - 2) (x + 3)$