# How do you simplify 2√3 (√3 - 1 )?

Jul 18, 2018

See a solution process below:

#### Explanation:

Expand the term in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{2 \sqrt{3}} \left(\sqrt{3} - 1\right) \implies$

$\left(\textcolor{red}{2 \sqrt{3}} \times \sqrt{3}\right) - \left(\textcolor{red}{2 \sqrt{3}} \times 1\right) \implies$

$\textcolor{red}{2} {\left(\sqrt{3}\right)}^{2} - 2 \sqrt{3} \implies$

$\left(\textcolor{red}{2} \times 3\right) - 2 \sqrt{3} \implies$

$6 - 2 \sqrt{3}$

$2 \setminus \sqrt{3} \left(\setminus \sqrt{3} - 1\right)$

$= \left(2 \setminus \sqrt{3}\right) \setminus \sqrt{3} - 2 \setminus \sqrt{3}$

$= 2 \left(\setminus \sqrt{3} \setminus \sqrt{3}\right) - 2 \setminus \sqrt{3}$

$= 2 \left(3\right) - 2 \setminus \sqrt{3}$

$= 6 - 2 \setminus \sqrt{3}$

Jul 18, 2018

$6 - 2 \sqrt{3}$

#### Explanation:

Distributing $2 \sqrt{3}$ to the parenthesis, we now have

$2 \textcolor{b l u e}{\sqrt{3} \sqrt{3}} - 2 \sqrt{3}$

This simplifies to

$2 \cdot \textcolor{b l u e}{3} - 2 \sqrt{3}$

$\implies 6 - 2 \sqrt{3}$

Hope this helps!