# How do you simplify  (sqrt5+4)(sqrt5-1)?

Apr 10, 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.

$\left(\textcolor{red}{\sqrt{5}} + \textcolor{red}{4}\right) \left(\textcolor{b l u e}{\sqrt{5}} - \textcolor{b l u e}{1}\right)$ becomes:

$\left(\textcolor{red}{\sqrt{5}} \times \textcolor{b l u e}{\sqrt{5}}\right) - \left(\textcolor{red}{\sqrt{5}} \times \textcolor{b l u e}{1}\right) + \left(\textcolor{red}{4} \times \textcolor{b l u e}{\sqrt{5}}\right) - \left(\textcolor{red}{4} \times \textcolor{b l u e}{1}\right)$

${\left(\sqrt{5}\right)}^{2} - \sqrt{5} + 4 \sqrt{5} - 4$

$5 - \sqrt{5} + 4 \sqrt{5} - 4$

We can now group and combine like terms:

$5 - 4 - 1 \sqrt{5} + 4 \sqrt{5}$

$\left(5 - 4\right) + \left(- 1 + 4\right) \sqrt{5}$

$1 + 3 \sqrt{5}$

Or

$3 \sqrt{5} + 1$

Apr 10, 2017

$1 + 3 \sqrt{5}$

#### Explanation:

$\left(\sqrt{5} + 4\right) \left(\sqrt{5} - 1\right) =$

$= 5 - \sqrt{5} + 4 \sqrt{5} - 4 =$

$= 1 + 3 \sqrt{5}$