Factor 8-27a^3

$8 - 27 a^{3}$

Step 1

Rewrite $8$ as $2^{3}$ .

$2^{3} - 27 a^{3}$

Step 2

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

$2^{3} - {(3 a)}^{3}$

Step 3

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

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

Step 4

Simplify.

Multiply $3$ by $- 1$ .

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

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

$(2 - 3 a) (4 + 2 (3 a) + {(3 a)}^{2})$

Multiply $3$ by $2$ .

$(2 - 3 a) (4 + 6 a + {(3 a)}^{2})$

Apply the product rule to $3 a$ .

$(2 - 3 a) (4 + 6 a + 3^{2} a^{2})$

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

$(2 - 3 a) (4 + 6 a + 9 a^{2})$

Factor 8-27a^3

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