Factor 54x^3-16

$54 x^{3} - 16$

Step 1

Factor $2$ out of $54 x^{3} - 16$ .

Factor $2$ out of $54 x^{3}$ .

$2 (27 x^{3}) - 16$

Factor $2$ out of $- 16$ .

$2 (27 x^{3}) + 2 (- 8)$

Factor $2$ out of $2 (27 x^{3}) + 2 (- 8)$ .

$2 (27 x^{3} - 8)$

Step 2

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

$2 ({(3 x)}^{3} - 8)$

Step 3

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

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

Step 4

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 $a = 3 x$ and $b = 2$ .

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

Step 5

Factor.

Simplify.

Apply the product rule to $3 x$ .

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

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

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

Multiply $2$ by $3$ .

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

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

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

Remove unnecessary parentheses.

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

Factor 54x^3-16

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