Pre-Algebra Examples

$\frac{r^{3} - s^{3}}{r - s}$

Step 1

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 $a = r$ and $b = s$ .

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

Step 2

Cancel the common factor of $r - s$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Divide $r^{2} + r s + s^{2}$ by $1$ .

$r^{2} + r s + s^{2}$