Pre-Algebra Examples

$\frac{a^{3} - b^{3}}{a - b}$

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

$\frac{(a - b) (a^{2} + a b + b^{2})}{a - b}$

Step 2

Cancel the common factor of $a - b$ .

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Step 2.1

Cancel the common factor.

$\frac{(a - b) (a^{2} + a b + b^{2})}{a - b}$

Step 2.2

Divide $a^{2} + a b + b^{2}$ by $1$ .

$a^{2} + a b + b^{2}$