Finite Math Examples

$s^{3} - \frac{1}{125}$

Step 1

Rewrite $\frac{1}{125}$ as ${(\frac{1}{5})}^{3}$ .

$s^{3} - {(\frac{1}{5})}^{3}$

Step 2

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 $a = s$ and $b = \frac{1}{5}$ .

$(s - \frac{1}{5}) (s^{2} + s \frac{1}{5} + {(\frac{1}{5})}^{2})$

Step 3

Simplify.

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Step 3.1

Combine $s$ and $\frac{1}{5}$ .

$(s - \frac{1}{5}) (s^{2} + \frac{s}{5} + {(\frac{1}{5})}^{2})$

Step 3.2

Apply the product rule to $\frac{1}{5}$ .

$(s - \frac{1}{5}) (s^{2} + \frac{s}{5} + \frac{1^{2}}{5^{2}})$

Step 3.3

One to any power is one.

$(s - \frac{1}{5}) (s^{2} + \frac{s}{5} + \frac{1}{5^{2}})$

Step 3.4

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

$(s - \frac{1}{5}) (s^{2} + \frac{s}{5} + \frac{1}{25})$

Step 3.5

Factor.

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Step 3.5.1

Factor $\frac{1}{25}$ out of each term.

$(s - \frac{1}{5}) (\frac{1}{25} (25 s^{2} + 5 s + 1))$

Step 3.5.2

Remove unnecessary parentheses.

$(s - \frac{1}{5}) \frac{1}{25} (25 s^{2} + 5 s + 1)$