Factor 16x^3-54

$16 x^{3} - 54$

Step 1

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

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

$2 (8 x^{3}) - 54$

Factor $2$ out of $- 54$ .

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

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

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

Step 2

Rewrite $8 x^{3}$ as ${(2 x)}^{3}$ .

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

Step 3

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

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

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

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

Step 5

Factor.

Simplify.

Apply the product rule to $2 x$ .

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

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

$2 ((2 x - 3) (4 x^{2} + 2 x \cdot 3 + 3^{2}))$

Multiply $3$ by $2$ .

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

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

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

Remove unnecessary parentheses.

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

Factor 16x^3-54

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