Algebra Examples

$64 x^{3} - 8$

Step 1

Factor $8$ out of $64 x^{3} - 8$ .

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Step 1.1

Factor $8$ out of $64 x^{3}$ .

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

Step 1.2

Factor $8$ out of $- 8$ .

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

Step 1.3

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

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

Step 2

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

$8 ({(2 x)}^{3} - 1)$

Step 3

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

$8 ({(2 x)}^{3} - 1^{3})$

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 $b = 1$ .

$8 ((2 x - 1) ({(2 x)}^{2} + 2 x \cdot 1 + 1^{2}))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Apply the product rule to $2 x$ .

$8 ((2 x - 1) (2^{2} x^{2} + 2 x \cdot 1 + 1^{2}))$

Step 5.1.2

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

$8 ((2 x - 1) (4 x^{2} + 2 x \cdot 1 + 1^{2}))$

Step 5.1.3

Multiply $2$ by $1$ .

$8 ((2 x - 1) (4 x^{2} + 2 x + 1^{2}))$

Step 5.1.4

One to any power is one.

$8 ((2 x - 1) (4 x^{2} + 2 x + 1))$

Step 5.2

Remove unnecessary parentheses.

$8 (2 x - 1) (4 x^{2} + 2 x + 1)$