Precalculus Examples

$250 x^{3} - 128$

Step 1

Factor $2$ out of $250 x^{3} - 128$ .

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Step 1.1

Factor $2$ out of $250 x^{3}$ .

$2 (125 x^{3}) - 128$

Step 1.2

Factor $2$ out of $- 128$ .

$2 (125 x^{3}) + 2 (- 64)$

Step 1.3

Factor $2$ out of $2 (125 x^{3}) + 2 (- 64)$ .

$2 (125 x^{3} - 64)$

Step 2

Rewrite $125 x^{3}$ as ${(5 x)}^{3}$ .

$2 ({(5 x)}^{3} - 64)$

Step 3

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

$2 ({(5 x)}^{3} - 4^{3})$

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 $a = 5 x$ and $b = 4$ .

$2 ((5 x - 4) ({(5 x)}^{2} + 5 x \cdot 4 + 4^{2}))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Apply the product rule to $5 x$ .

$2 ((5 x - 4) (5^{2} x^{2} + 5 x \cdot 4 + 4^{2}))$

Step 5.1.2

Raise $5$ to the power of $2$ .

$2 ((5 x - 4) (25 x^{2} + 5 x \cdot 4 + 4^{2}))$

Step 5.1.3

Multiply $4$ by $5$ .

$2 ((5 x - 4) (25 x^{2} + 20 x + 4^{2}))$

Step 5.1.4

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

$2 ((5 x - 4) (25 x^{2} + 20 x + 16))$

Step 5.2

Remove unnecessary parentheses.

$2 (5 x - 4) (25 x^{2} + 20 x + 16)$