Factor 128x^3-2 - MathMaster

$128 x^{3} - 2$

Factor $2$ out of $128 x^{3} - 2$ .

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Factor $2$ out of $128 x^{3}$ .

$2 (64 x^{3}) - 2$

Factor $2$ out of $- 2$ .

$2 (64 x^{3}) + 2 (- 1)$

Factor $2$ out of $2 (64 x^{3}) + 2 (- 1)$ .

$2 (64 x^{3} - 1)$

Rewrite $64 x^{3}$ as ${(4 x)}^{3}$ .

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

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

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

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 $a = 4 x$ and $b = 1$ .

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

Factor.

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Simplify.

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Apply the product rule to $4 x$ .

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

Raise $4$ to the power of $2$ .

$2 ((4 x - 1) (16 x^{2} + 4 x \cdot 1 + 1^{2}))$

Multiply $4$ by $1$ .

$2 ((4 x - 1) (16 x^{2} + 4 x + 1^{2}))$

One to any power is one.

$2 ((4 x - 1) (16 x^{2} + 4 x + 1))$

Remove unnecessary parentheses.

$2 (4 x - 1) (16 x^{2} + 4 x + 1)$

Factor 128x^3-2

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