Pre-Algebra Examples

$125 - a^{3}$

Step 1

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

$5^{3} - a^{3}$

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

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

Step 3

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

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