Algebra Examples

$27 - 8 x^{3}$

Step 1

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

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

Step 2

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

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

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

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

Step 4

Simplify.

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Step 4.1

Multiply $2$ by $- 1$ .

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

Step 4.2

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

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

Step 4.3

Multiply $2$ by $3$ .

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

Step 4.4

Apply the product rule to $2 x$ .

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

Step 4.5

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

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