Divide (x^3+216)/(x+6)

$\frac{x^{3} + 216}{x + 6}$

Step 1

Simplify the numerator.

Rewrite $216$ as $6^{3}$ .

$\frac{x^{3} + 6^{3}}{x + 6}$

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 $a = x$ and $b = 6$ .

$\frac{(x + 6) (x^{2} - x \cdot 6 + 6^{2})}{x + 6}$

Simplify.

Multiply $6$ by $- 1$ .

$\frac{(x + 6) (x^{2} - 6 x + 6^{2})}{x + 6}$

Raise $6$ to the power of $2$ .

$\frac{(x + 6) (x^{2} - 6 x + 36)}{x + 6}$

Step 2

Cancel the common factor of $x + 6$ .

Cancel the common factor.

$\frac{(x + 6) (x^{2} - 6 x + 36)}{x + 6}$

Divide $x^{2} - 6 x + 36$ by $1$ .

$x^{2} - 6 x + 36$

Divide (x^3+216)/(x+6)

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