Algebra Examples

$v^{3} - 125$

Step 1

Rewrite $125$ as $5^{3}$ .

$v^{3} - 5^{3}$

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 $a = v$ and $b = 5$ .

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

Step 3

Simplify.

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Step 3.1

Move $5$ to the left of $v$ .

$(v - 5) (v^{2} + 5 v + 5^{2})$

Step 3.2

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

$(v - 5) (v^{2} + 5 v + 25)$