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 difference 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.

Move $6$ to the left of $x$ .

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

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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