( sqrt 3 + 2 sqrt 10) (4 sqrt 3 - sqrt 10) How to multiply?

Apr 12, 2017

See the entire solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{\sqrt{3}} + \textcolor{red}{2 \sqrt{10}}\right) \left(\textcolor{b l u e}{4 \sqrt{3}} - \textcolor{b l u e}{\sqrt{10}}\right)$ becomes:

$\left(\textcolor{red}{\sqrt{3}} \times \textcolor{b l u e}{4 \sqrt{3}}\right) - \left(\textcolor{red}{\sqrt{3}} \times \textcolor{b l u e}{\sqrt{10}}\right) + \left(\textcolor{red}{2 \sqrt{10}} \times \textcolor{b l u e}{4 \sqrt{3}}\right) - \left(\textcolor{red}{2 \sqrt{10}} \times \textcolor{b l u e}{\sqrt{10}}\right)$

$4 {\left(\sqrt{3}\right)}^{2} - \sqrt{30} + 8 \sqrt{30} - 2 {\left(\sqrt{10}\right)}^{2}$

$\left(4 \cdot 3\right) - \sqrt{30} + 8 \sqrt{30} - \left(2 \cdot 10\right)$

$12 - \sqrt{30} + 8 \sqrt{30} - 20$

We can now group and combine like terms:

$12 - 20 - 1 \sqrt{30} + 8 \sqrt{30}$

$\left(12 - 20\right) + \left(- 1 + 8\right) \sqrt{30}$

$- 8 + 7 \sqrt{30}$

Or

$7 \sqrt{30} - 8$