Algebra Examples

$12 (4 - x^{2}) - 2 x (4 - x^{2}) - {(4 - x^{2})}^{2}$

Step 1

Factor $- (- x^{2} + 4)$ out of $12 (4 - x^{2}) - 2 x (4 - x^{2}) - {(4 - x^{2})}^{2}$ .

Tap for more steps...

Step 1.1

Reorder the expression.

Tap for more steps...

Step 1.1.1

Reorder $4$ and $- x^{2}$ .

$12 (- x^{2} + 4) - 2 x (4 - x^{2}) - {(4 - x^{2})}^{2}$

Step 1.1.2

Reorder $4$ and $- x^{2}$ .

$12 (- x^{2} + 4) - 2 x (- x^{2} + 4) - {(4 - x^{2})}^{2}$

Step 1.1.3

Reorder $4$ and $- x^{2}$ .

$12 (- x^{2} + 4) - 2 x (- x^{2} + 4) - {(- x^{2} + 4)}^{2}$

Step 1.1.4

Move $12 (- x^{2} + 4)$ .

$- 2 x (- x^{2} + 4) - {(- x^{2} + 4)}^{2} + 12 (- x^{2} + 4)$

Step 1.1.5

Reorder $- 2 x (- x^{2} + 4)$ and $- {(- x^{2} + 4)}^{2}$ .

$- {(- x^{2} + 4)}^{2} - 2 x (- x^{2} + 4) + 12 (- x^{2} + 4)$

Step 1.2

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

$- (- x^{2} + 4) (- x^{2} + 4) - 2 x (- x^{2} + 4) + 12 (- x^{2} + 4)$

Step 1.3

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

$- (- x^{2} + 4) (- x^{2} + 4) - (- x^{2} + 4) (2 x) + 12 (- x^{2} + 4)$

Step 1.4

Factor $- (- x^{2} + 4)$ out of $12 (- x^{2} + 4)$ .

$- (- x^{2} + 4) (- x^{2} + 4) - (- x^{2} + 4) (2 x) - (- x^{2} + 4) (- 12)$

Step 1.5

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

$- (- x^{2} + 4) (- x^{2} + 4 + 2 x) - (- x^{2} + 4) (- 12)$

Step 1.6

Factor $- (- x^{2} + 4)$ out of $- (- x^{2} + 4) (- x^{2} + 4 + 2 x) - (- x^{2} + 4) (- 12)$ .

$- (- x^{2} + 4) (- x^{2} + 4 + 2 x - 12)$

Step 2

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

$- (- x^{2} + 2^{2}) (- x^{2} + 4 + 2 x - 12)$

Step 3

Reorder $- x^{2}$ and $2^{2}$ .

$- (2^{2} - x^{2}) (- x^{2} + 4 + 2 x - 12)$

Step 4

Factor.

Tap for more steps...

Step 4.1

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

$- ((2 + x) (2 - x)) (- x^{2} + 4 + 2 x - 12)$

Step 4.2

Remove unnecessary parentheses.

$- (2 + x) (2 - x) (- x^{2} + 4 + 2 x - 12)$

Step 5

Subtract $12$ from $4$ .

$- (2 + x) (2 - x) (- x^{2} + 2 x - 8)$

Step 6

Factor.

Tap for more steps...

Step 6.1

Factor $- 1$ out of $- x^{2} + 2 x - 8$ .

Tap for more steps...

Step 6.1.1

Factor $- 1$ out of $- x^{2}$ .

$- (2 + x) (2 - x) (- (x^{2}) + 2 x - 8)$

Step 6.1.2

Factor $- 1$ out of $2 x$ .

$- (2 + x) (2 - x) (- (x^{2}) - (- 2 x) - 8)$

Step 6.1.3

Rewrite $- 8$ as $- 1 (8)$ .

$- (2 + x) (2 - x) (- (x^{2}) - (- 2 x) - 1 (8))$

Step 6.1.4

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

$- (2 + x) (2 - x) (- (x^{2} - 2 x) - 1 (8))$

Step 6.1.5

Factor $- 1$ out of $- (x^{2} - 2 x) - 1 (8)$ .

$- (2 + x) (2 - x) (- (x^{2} - 2 x + 8))$

Step 6.2

Remove unnecessary parentheses.

$- (2 + x) (2 - x) \cdot - 1 (x^{2} - 2 x + 8)$

Step 7

Combine exponents.

Tap for more steps...

Step 7.1

Factor out negative.

$- (((2 + x) (2 - x)) \cdot - 1 (x^{2} - 2 x + 8))$

Step 7.2

Multiply $- 1$ by $- 1$ .

$1 (((2 + x) (2 - x)) (x^{2} - 2 x + 8))$

Step 7.3

Multiply $2 + x$ by $1$ .

$(2 + x) ((2 - x) (x^{2} - 2 x + 8))$

Step 8

Remove unnecessary parentheses.

$(2 + x) (2 - x) (x^{2} - 2 x + 8)$