Factor 32x^3-4

$32 x^{3} - 4$

Step 1

Factor $4$ out of $32 x^{3} - 4$ .

Factor $4$ out of $32 x^{3}$ .

$4 (8 x^{3}) - 4$

Factor $4$ out of $- 4$ .

$4 (8 x^{3}) + 4 (- 1)$

Factor $4$ out of $4 (8 x^{3}) + 4 (- 1)$ .

$4 (8 x^{3} - 1)$

Step 2

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

$4 ({(2 x)}^{3} - 1)$

Step 3

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

$4 ({(2 x)}^{3} - 1^{3})$

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 $b = 1$ .

$4 ((2 x - 1) ({(2 x)}^{2} + 2 x \cdot 1 + 1^{2}))$

Step 5

Factor.

Simplify.

Apply the product rule to $2 x$ .

$4 ((2 x - 1) (2^{2} x^{2} + 2 x \cdot 1 + 1^{2}))$

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

$4 ((2 x - 1) (4 x^{2} + 2 x \cdot 1 + 1^{2}))$

Multiply $2$ by $1$ .

$4 ((2 x - 1) (4 x^{2} + 2 x + 1^{2}))$

One to any power is one.

$4 ((2 x - 1) (4 x^{2} + 2 x + 1))$

Remove unnecessary parentheses.

$4 (2 x - 1) (4 x^{2} + 2 x + 1)$

Factor 32x^3-4

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