Algebra Examples

$v^{4} - 1$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify.

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Step 4.1

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

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

Step 4.2

Factor.

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Step 4.2.1

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

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

Step 4.2.2

Remove unnecessary parentheses.

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