Divide (a^3+8)/(a+2)

$\frac{a^{3} + 8}{a + 2}$

Simplify the numerator.

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Rewrite $8$ as $2^{3}$ .

$\frac{a^{3} + 2^{3}}{a + 2}$

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 $a = a$ and $b = 2$ .

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

Simplify.

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Multiply $2$ by $- 1$ .

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

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

$\frac{(a + 2) (a^{2} - 2 a + 4)}{a + 2}$

Cancel the common factor of $a + 2$ .

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Cancel the common factor.

$\frac{(a + 2) (a^{2} - 2 a + 4)}{a + 2}$

Divide $a^{2} - 2 a + 4$ by $1$ .

$a^{2} - 2 a + 4$

Divide (a^3+8)/(a+2)

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