Pre-Algebra Examples

$72 m^{4} - 128$

Step 1

Factor $8$ out of $72 m^{4} - 128$ .

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Step 1.1

Factor $8$ out of $72 m^{4}$ .

$8 (9 m^{4}) - 128$

Step 1.2

Factor $8$ out of $- 128$ .

$8 (9 m^{4}) + 8 (- 16)$

Step 1.3

Factor $8$ out of $8 (9 m^{4}) + 8 (- 16)$ .

$8 (9 m^{4} - 16)$

Step 2

Rewrite $9 m^{4}$ as ${(3 m^{2})}^{2}$ .

$8 ({(3 m^{2})}^{2} - 16)$

Step 3

Rewrite $16$ as $4^{2}$ .

$8 ({(3 m^{2})}^{2} - 4^{2})$

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 $a = 3 m^{2}$ and $b = 4$ .

$8 ((3 m^{2} + 4) (3 m^{2} - 4))$

Step 4.2

Remove unnecessary parentheses.

$8 (3 m^{2} + 4) (3 m^{2} - 4)$