Basic Math Examples

$2 c^{3} - 16$

Step 1

Factor $2$ out of $2 c^{3} - 16$ .

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Step 1.1

Factor $2$ out of $2 c^{3}$ .

$2 (c^{3}) - 16$

Step 1.2

Factor $2$ out of $- 16$ .

$2 c^{3} + 2 \cdot - 8$

Step 1.3

Factor $2$ out of $2 c^{3} + 2 \cdot - 8$ .

$2 (c^{3} - 8)$

Step 2

Rewrite $8$ as $2^{3}$ .

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

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 $a = c$ and $b = 2$ .

$2 ((c - 2) (c^{2} + c \cdot 2 + 2^{2}))$

Step 4

Factor.

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Step 4.1

Simplify.

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Step 4.1.1

Move $2$ to the left of $c$ .

$2 ((c - 2) (c^{2} + 2 c + 2^{2}))$

Step 4.1.2

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

$2 ((c - 2) (c^{2} + 2 c + 4))$

Step 4.2

Remove unnecessary parentheses.

$2 (c - 2) (c^{2} + 2 c + 4)$