Algebra Examples

$81 v^{4} - 900 v^{2}$

Step 1

Factor $9 v^{2}$ out of $81 v^{4} - 900 v^{2}$ .

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Step 1.1

Factor $9 v^{2}$ out of $81 v^{4}$ .

$9 v^{2} (9 v^{2}) - 900 v^{2}$

Step 1.2

Factor $9 v^{2}$ out of $- 900 v^{2}$ .

$9 v^{2} (9 v^{2}) + 9 v^{2} (- 100)$

Step 1.3

Factor $9 v^{2}$ out of $9 v^{2} (9 v^{2}) + 9 v^{2} (- 100)$ .

$9 v^{2} (9 v^{2} - 100)$

Step 2

Rewrite $9 v^{2}$ as ${(3 v)}^{2}$ .

$9 v^{2} ({(3 v)}^{2} - 100)$

Step 3

Rewrite $100$ as $10^{2}$ .

$9 v^{2} ({(3 v)}^{2} - 10^{2})$

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 $a = 3 v$ and $b = 10$ .

$9 v^{2} ((3 v + 10) (3 v - 10))$

Step 4.2

Remove unnecessary parentheses.

$9 v^{2} (3 v + 10) (3 v - 10)$