Factor 3x^3+81

$3 x^{3} + 81$

Step 1

Factor $3$ out of $3 x^{3} + 81$ .

Factor $3$ out of $3 x^{3}$ .

$3 (x^{3}) + 81$

Factor $3$ out of $81$ .

$3 x^{3} + 3 \cdot 27$

Factor $3$ out of $3 x^{3} + 3 \cdot 27$ .

$3 (x^{3} + 27)$

Step 2

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

$3 (x^{3} + 3^{3})$

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 $a = x$ and $b = 3$ .

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

Step 4

Factor.

Simplify.

Multiply $3$ by $- 1$ .

$3 ((x + 3) (x^{2} - 3 x + 3^{2}))$

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

$3 ((x + 3) (x^{2} - 3 x + 9))$

Remove unnecessary parentheses.

$3 (x + 3) (x^{2} - 3 x + 9)$

Factor 3x^3+81

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