Algebra Examples

$400 - 36 v^{2}$

Step 1

Factor $4$ out of $400 - 36 v^{2}$ .

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Step 1.1

Factor $4$ out of $400$ .

$4 (100) - 36 v^{2}$

Step 1.2

Factor $4$ out of $- 36 v^{2}$ .

$4 (100) + 4 (- 9 v^{2})$

Step 1.3

Factor $4$ out of $4 (100) + 4 (- 9 v^{2})$ .

$4 (100 - 9 v^{2})$

Step 2

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

$4 (10^{2} - 9 v^{2})$

Step 3

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

$4 (10^{2} - {(3 v)}^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 10$ and $b = 3 v$ .

$4 ((10 + 3 v) (10 - (3 v)))$

Step 5

Factor.

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Step 5.1

Multiply $3$ by $- 1$ .

$4 ((10 + 3 v) (10 - 3 v))$

Step 5.2

Remove unnecessary parentheses.

$4 (10 + 3 v) (10 - 3 v)$