Pre-Algebra Examples

$(k^{3} - 1) \div (k - 1)$

Step 1

Rewrite the division as a fraction.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Simplify.

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Step 2.3.1

Multiply $k$ by $1$ .

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

Step 2.3.2

One to any power is one.

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

Step 3

Cancel the common factor of $k - 1$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

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

$k^{2} + k + 1$