Factor 27b^3+1

$27 b^{3} + 1$

Step 1

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

${(3 b)}^{3} + 1$

Step 2

Rewrite $1$ as $1^{3}$ .

${(3 b)}^{3} + 1^{3}$

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 $a = 3 b$ and $b = 1$ .

$(3 b + 1) ({(3 b)}^{2} - (3 b) \cdot 1 + 1^{2})$

Step 4

Simplify.

Apply the product rule to $3 b$ .

$(3 b + 1) (3^{2} b^{2} - (3 b) \cdot 1 + 1^{2})$

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

$(3 b + 1) (9 b^{2} - (3 b) \cdot 1 + 1^{2})$

Multiply $3$ by $- 1$ .

$(3 b + 1) (9 b^{2} - 3 b \cdot 1 + 1^{2})$

Multiply $- 3$ by $1$ .

$(3 b + 1) (9 b^{2} - 3 b + 1^{2})$

One to any power is one.

$(3 b + 1) (9 b^{2} - 3 b + 1)$

Factor 27b^3+1

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