Pre-Algebra Examples

$48 u - 75 u^{3}$

Step 1

Factor $3 u$ out of $48 u - 75 u^{3}$ .

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Step 1.1

Factor $3 u$ out of $48 u$ .

$3 u (16) - 75 u^{3}$

Step 1.2

Factor $3 u$ out of $- 75 u^{3}$ .

$3 u (16) + 3 u (- 25 u^{2})$

Step 1.3

Factor $3 u$ out of $3 u (16) + 3 u (- 25 u^{2})$ .

$3 u (16 - 25 u^{2})$

Step 2

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

$3 u (4^{2} - 25 u^{2})$

Step 3

Rewrite $25 u^{2}$ as ${(5 u)}^{2}$ .

$3 u (4^{2} - {(5 u)}^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4$ and $b = 5 u$ .

$3 u ((4 + 5 u) (4 - (5 u)))$

Step 5

Factor.

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Step 5.1

Multiply $5$ by $- 1$ .

$3 u ((4 + 5 u) (4 - 5 u))$

Step 5.2

Remove unnecessary parentheses.

$3 u (4 + 5 u) (4 - 5 u)$