Pre-Algebra Examples

$2 w^{2} - 2 w^{2} x^{4}$

Step 1

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

Tap for more steps...

Step 1.1

Factor $2 w^{2}$ out of $2 w^{2}$ .

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

Step 1.2

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

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

Step 1.3

Factor $2 w^{2}$ out of $2 w^{2} (1) + 2 w^{2} (- 1 x^{4})$ .

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

Step 2

Rewrite $1$ as $1^{2}$ .

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

Step 3

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x^{2}$ .

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

Step 5

Factor.

Tap for more steps...

Step 5.1

Simplify.

Tap for more steps...

Step 5.1.1

Rewrite $1$ as $1^{2}$ .

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

Step 5.1.2

Factor.

Tap for more steps...

Step 5.1.2.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x$ .

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

Step 5.1.2.2

Remove unnecessary parentheses.

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

Step 5.2

Remove unnecessary parentheses.

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