How do you factor the expression 3x^3-27x?

Mar 19, 2018

See a solution process below:

Explanation:

First, we can rewrite and factor as $x 3$ out of this expression as:

$\left(3 x \cdot {x}^{2}\right) - \left(3 x \cdot 9\right) \implies$

$3 x \left({x}^{2} - 9\right)$

Now we can use this formula for the special case of this quadratic to complete the factoring:

${\textcolor{red}{x}}^{2} - {\textcolor{b l u e}{y}}^{2} = \left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right) \left(\textcolor{red}{x} - \textcolor{b l u e}{y}\right)$

$3 x \left({x}^{2} - 9\right) \implies$

$3 x \left({\textcolor{red}{x}}^{2} - {\textcolor{b l u e}{3}}^{2}\right) \implies$

$3 x \left(\textcolor{red}{x} + \textcolor{b l u e}{3}\right) \left(\textcolor{red}{x} - \textcolor{b l u e}{3}\right)$