Algebra Examples

$64 + 27 x^{3}$

Step 1

Rewrite $64$ as $4^{3}$ .

$4^{3} + 27 x^{3}$

Step 2

Rewrite $27 x^{3}$ as ${(3 x)}^{3}$ .

$4^{3} + {(3 x)}^{3}$

Step 3

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = 4$ and $b = 3 x$ .

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

Step 4

Simplify.

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Step 4.1

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

$(4 + 3 x) (16 - 4 (3 x) + {(3 x)}^{2})$

Step 4.2

Multiply $3$ by $- 4$ .

$(4 + 3 x) (16 - 12 x + {(3 x)}^{2})$

Step 4.3

Apply the product rule to $3 x$ .

$(4 + 3 x) (16 - 12 x + 3^{2} x^{2})$

Step 4.4

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

$(4 + 3 x) (16 - 12 x + 9 x^{2})$