Basic Math Examples

$b f^{3} + 27 b$

Step 1

Factor $b$ out of $b f^{3} + 27 b$ .

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Step 1.1

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

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

Step 1.2

Factor $b$ out of $27 b$ .

$b (f^{3}) + b \cdot 27$

Step 1.3

Factor $b$ out of $b (f^{3}) + b \cdot 27$ .

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

Step 2

Rewrite $27$ as $3^{3}$ .

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

Step 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 $a = f$ and $b = 3$ .

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

Step 4

Factor.

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Step 4.1

Simplify.

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Step 4.1.1

Multiply $3$ by $- 1$ .

$b ((f + 3) (f^{2} - 3 f + 3^{2}))$

Step 4.1.2

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

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

Step 4.2

Remove unnecessary parentheses.

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