Algebra Examples

$(36 a^{2} - 64 b^{2})$

Step 1

Remove parentheses.

$36 a^{2} - 64 b^{2}$

Step 2

Factor $4$ out of $36 a^{2} - 64 b^{2}$ .

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Step 2.1

Factor $4$ out of $36 a^{2}$ .

$4 (9 a^{2}) - 64 b^{2}$

Step 2.2

Factor $4$ out of $- 64 b^{2}$ .

$4 (9 a^{2}) + 4 (- 16 b^{2})$

Step 2.3

Factor $4$ out of $4 (9 a^{2}) + 4 (- 16 b^{2})$ .

$4 (9 a^{2} - 16 b^{2})$

Step 3

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

$4 ({(3 a)}^{2} - 16 b^{2})$

Step 4

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

$4 ({(3 a)}^{2} - {(4 b)}^{2})$

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 a$ and $b = 4 b$ .

$4 ((3 a + 4 b) (3 a - (4 b)))$

Step 6

Factor.

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Step 6.1

Multiply $4$ by $- 1$ .

$4 ((3 a + 4 b) (3 a - 4 b))$

Step 6.2

Remove unnecessary parentheses.

$4 (3 a + 4 b) (3 a - 4 b)$