Basic Math Examples

$\frac{z^{3} + 27}{z + 3}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $27$ as $3^{3}$ .

$\frac{z^{3} + 3^{3}}{z + 3}$

Step 1.2

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = z$ and $b = 3$ .

$\frac{(z + 3) (z^{2} - z \cdot 3 + 3^{2})}{z + 3}$

Step 1.3

Simplify.

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Step 1.3.1

Multiply $3$ by $- 1$ .

$\frac{(z + 3) (z^{2} - 3 z + 3^{2})}{z + 3}$

Step 1.3.2

Raise $3$ to the power of $2$ .

$\frac{(z + 3) (z^{2} - 3 z + 9)}{z + 3}$

Step 2

Cancel the common factor of $z + 3$ .

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Step 2.1

Cancel the common factor.

$\frac{(z + 3) (z^{2} - 3 z + 9)}{z + 3}$

Step 2.2

Divide $z^{2} - 3 z + 9$ by $1$ .

$z^{2} - 3 z + 9$