Algebra Examples

$32 x^{2} - 2$

Step 1

Factor $2$ out of $32 x^{2} - 2$ .

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Step 1.1

Factor $2$ out of $32 x^{2}$ .

$2 (16 x^{2}) - 2$

Step 1.2

Factor $2$ out of $- 2$ .

$2 (16 x^{2}) + 2 (- 1)$

Step 1.3

Factor $2$ out of $2 (16 x^{2}) + 2 (- 1)$ .

$2 (16 x^{2} - 1)$

Step 2

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

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

Step 3

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

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

Step 4

Factor.

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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 $a = 4 x$ and $b = 1$ .

$2 ((4 x + 1) (4 x - 1))$

Step 4.2

Remove unnecessary parentheses.

$2 (4 x + 1) (4 x - 1)$