Factor 81b^3+192 - Math solver

$81 b^{3} + 192$

Factor $3$ out of $81 b^{3} + 192$ .

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Factor $3$ out of $81 b^{3}$ .

$3 (27 b^{3}) + 192$

Factor $3$ out of $192$ .

$3 (27 b^{3}) + 3 (64)$

Factor $3$ out of $3 (27 b^{3}) + 3 (64)$ .

$3 (27 b^{3} + 64)$

Rewrite $27 b^{3}$ as ${(3 b)}^{3}$ .

$3 ({(3 b)}^{3} + 64)$

Rewrite $64$ as $4^{3}$ .

$3 ({(3 b)}^{3} + 4^{3})$

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

$3 ((3 b + 4) ({(3 b)}^{2} - (3 b) \cdot 4 + 4^{2}))$

Factor.

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Simplify.

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Apply the product rule to $3 b$ .

$3 ((3 b + 4) (3^{2} b^{2} - (3 b) \cdot 4 + 4^{2}))$

Raise $3$ to the power of $2$ .

$3 ((3 b + 4) (9 b^{2} - (3 b) \cdot 4 + 4^{2}))$

Multiply $3$ by $- 1$ .

$3 ((3 b + 4) (9 b^{2} - 3 b \cdot 4 + 4^{2}))$

Multiply $4$ by $- 3$ .

$3 ((3 b + 4) (9 b^{2} - 12 b + 4^{2}))$

Raise $4$ to the power of $2$ .

$3 ((3 b + 4) (9 b^{2} - 12 b + 16))$

Remove unnecessary parentheses.

$3 (3 b + 4) (9 b^{2} - 12 b + 16)$

Factor 81b^3+192