How do you simplify (sqrt2-3)(sqrt6+5)?

1 Answer
Jul 15, 2017

See a 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.

$\left(\textcolor{red}{\sqrt{2}} - \textcolor{red}{3}\right) \left(\textcolor{b l u e}{\sqrt{6}} + \textcolor{b l u e}{5}\right)$ becomes:

$\left(\textcolor{red}{\sqrt{2}} \times \textcolor{b l u e}{\sqrt{6}}\right) + \left(\textcolor{red}{\sqrt{2}} \times \textcolor{b l u e}{5}\right) - \left(\textcolor{red}{3} \times \textcolor{b l u e}{\sqrt{6}}\right) - \left(\textcolor{red}{3} \times \textcolor{b l u e}{5}\right)$

$\sqrt{\textcolor{red}{2} \cdot \textcolor{b l u e}{6}} + 5 \sqrt{2} - 3 \sqrt{6} - 15$

$\sqrt{12} + 5 \sqrt{2} - 3 \sqrt{6} - 15$

$\sqrt{4 \cdot 3} + 5 \sqrt{2} - 3 \sqrt{6} - 15$

$\sqrt{4} \sqrt{3} + 5 \sqrt{2} - 3 \sqrt{6} - 15$

$2 \sqrt{3} + 5 \sqrt{2} - 3 \sqrt{6} - 15$