Simplify (x^3-27)/(x-3)

$\frac{x^{3} - 27}{x - 3}$

Step 1

Simplify the numerator.

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

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

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 $b = 3$ .

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

Simplify.

Move $3$ to the left of $x$ .

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

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

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

Step 2

Cancel the common factor of $x - 3$ .

Cancel the common factor.

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

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

$x^{2} + 3 x + 9$

Simplify (x^3-27)/(x-3)

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