# How do you simplify 2x(x^2-3)?

Apr 17, 2017

See the entire solution process below:

#### Explanation:

To simplify this expression multiply each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{2 x} \left({x}^{2} - 3\right) = \left(\textcolor{red}{2 x} \times {x}^{2}\right) - \left(\textcolor{red}{2 x} \times 3\right) = 2 {x}^{3} - 6 x$

Apr 17, 2017

$2 {x}^{3} - 6 x$

#### Explanation:

Apply the distributive property

$\textcolor{red}{2 x} \left({x}^{2} - 3\right) = \textcolor{red}{2 x} \left({x}^{2}\right) - \textcolor{red}{2 x} \left(3\right)$

$\textcolor{red}{2 x}$ is the same as $\textcolor{red}{2 {x}^{1}}$

So $\textcolor{red}{2 x} \left({x}^{2}\right) - \textcolor{red}{2 x} \left(3\right) = \textcolor{red}{2 {x}^{\textcolor{g r e e n}{1}}} \left({x}^{2}\right) - \textcolor{red}{2 x} \left(3\right)$

To multiply $\textcolor{red}{2 {x}^{\textcolor{g r e e n}{1}}}$ and ${x}^{2}$ add the exponents of the $x$ terms, so,

$\textcolor{red}{2 {x}^{\textcolor{g r e e n}{1}}} \left({x}^{2}\right) = 2 {x}^{\textcolor{g r e e n}{1} + 2} = 2 {x}^{3}$

$\textcolor{red}{2 {x}^{\textcolor{g r e e n}{1}}} \left({x}^{2}\right) - \textcolor{red}{2 x} \left(3\right) = 2 {x}^{3} - 6 x$