Question

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

Answer 1

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

Explanation:

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

Thus, since `x^3-27=x^3-3^3`,

`(x^3-27)/(x-3)=((x-3)(x^2+3x+9))/(x-3)=((cancel(x-3))(x^2+3x+9))/(cancel(x-3))=x^2+3x+9`

This last equality is true as long as `x!=3`.