# How do you simplify (x³-27 )/ (x-3)?

Oct 20, 2015

Use the formula for the difference of two cubes to factor the top and cancel the $x - 3$ to get ${x}^{2} + 3 x + 9$

#### Explanation:

The formula for the difference of two cubes is ${a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$ (check this by expanding out the right side).

Thus, since ${x}^{3} - 27 = {x}^{3} - {3}^{3}$,

$\frac{{x}^{3} - 27}{x - 3} = \frac{\left(x - 3\right) \left({x}^{2} + 3 x + 9\right)}{x - 3} = \frac{\left(\cancel{x - 3}\right) \left({x}^{2} + 3 x + 9\right)}{\cancel{x - 3}} = {x}^{2} + 3 x + 9$

This last equality is true as long as $x \ne 3$.