Basic Math Examples

$2 v^{4} b^{4} - 2 v^{4}$

Step 1

Factor $2 v^{4}$ out of $2 v^{4} b^{4} - 2 v^{4}$ .

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Step 1.1

Factor $2 v^{4}$ out of $2 v^{4} b^{4}$ .

$2 v^{4} (b^{4}) - 2 v^{4}$

Step 1.2

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

$2 v^{4} (b^{4}) + 2 v^{4} (- 1)$

Step 1.3

Factor $2 v^{4}$ out of $2 v^{4} (b^{4}) + 2 v^{4} (- 1)$ .

$2 v^{4} (b^{4} - 1)$

Step 2

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

$2 v^{4} ({(b^{2})}^{2} - 1)$

Step 3

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

$2 v^{4} ({(b^{2})}^{2} - 1^{2})$

Step 4

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

$2 v^{4} ((b^{2} + 1) (b^{2} - 1))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

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

$2 v^{4} ((b^{2} + 1) (b^{2} - 1^{2}))$

Step 5.1.2

Factor.

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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 $a = b$ and $b = 1$ .

$2 v^{4} ((b^{2} + 1) ((b + 1) (b - 1)))$

Step 5.1.2.2

Remove unnecessary parentheses.

$2 v^{4} ((b^{2} + 1) (b + 1) (b - 1))$

Step 5.2

Remove unnecessary parentheses.

$2 v^{4} (b^{2} + 1) (b + 1) (b - 1)$