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

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

Step 1

Simplify the numerator.

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

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

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 $b = 6$ .

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

Simplify.

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

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

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

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

Step 2

Cancel the common factor of $x - 6$ and $6 - x$ .

Factor $- 1$ out of $x$ .

$\frac{(- 1 (- x) - 6) (x^{2} + 6 x + 36)}{6 - x}$

Rewrite $- 6$ as $- 1 (6)$ .

$\frac{(- 1 (- x) - 1 (6)) (x^{2} + 6 x + 36)}{6 - x}$

Factor $- 1$ out of $- 1 (- x) - 1 (6)$ .

$\frac{- 1 (- x + 6) (x^{2} + 6 x + 36)}{6 - x}$

Reorder terms.

$\frac{- 1 (- x + 6) (x^{2} + 6 x + 36)}{- x + 6}$

Cancel the common factor.

$\frac{- 1 (- x + 6) (x^{2} + 6 x + 36)}{- x + 6}$

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

$- 1 (x^{2} + 6 x + 36)$

Step 3

Rewrite $- 1 (x^{2} + 6 x + 36)$ as $- (x^{2} + 6 x + 36)$ .

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

Step 4

Apply the distributive property.

$- x^{2} - (6 x) - 1 \cdot 36$

Step 5

Simplify.

Multiply $6$ by $- 1$ .

$- x^{2} - 6 x - 1 \cdot 36$

Multiply $- 1$ by $36$ .

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

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

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