Algebra Examples

determine the factors of $144 x^{2} - 64$

Step 1

Factor $16$ out of $144 x^{2} - 64$ .

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Step 1.1

Factor $16$ out of $144 x^{2}$ .

$16 (9 x^{2}) - 64$

Step 1.2

Factor $16$ out of $- 64$ .

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

Step 1.3

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

$16 (9 x^{2} - 4)$

Step 2

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

$16 ({(3 x)}^{2} - 4)$

Step 3

Rewrite $4$ as $2^{2}$ .

$16 ({(3 x)}^{2} - 2^{2})$

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 $a = 3 x$ and $b = 2$ .

$16 ((3 x + 2) (3 x - 2))$

Step 4.2

Remove unnecessary parentheses.

$16 (3 x + 2) (3 x - 2)$