Pre-Algebra Examples

$\frac{a^{3} - 1}{a - 1}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite $1$ as $1^{3}$ .

$\frac{a^{3} - 1^{3}}{a - 1}$

Step 1.2

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 $a = a$ and $b = 1$ .

$\frac{(a - 1) (a^{2} + a \cdot 1 + 1^{2})}{a - 1}$

Step 1.3

Simplify.

Tap for more steps...

Step 1.3.1

Multiply $a$ by $1$ .

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

Step 1.3.2

One to any power is one.

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

Step 2

Cancel the common factor of $a - 1$ .

Tap for more steps...

Step 2.1

Cancel the common factor.

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

Step 2.2

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

$a^{2} + a + 1$