# How do you simplify (3+sqrt7)(3-sqrt7)?

Sep 6, 2015

$\left(3 + \sqrt{7}\right) \left(3 - \sqrt{7}\right) = 2$

#### Explanation:

You can simplify this expression by using the formula for the difference of squares

$\textcolor{b l u e}{{a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)}$

In your case, you ca say that $a = 3$ and $b = \sqrt{7}$. This means that you have

$\left(3 + \sqrt{7}\right) \left(3 - \sqrt{7}\right) = {3}^{2} - {\left(\sqrt{7}\right)}^{2} = 9 - 7 = \textcolor{g r e e n}{2}$

Alternatively, if you don't know the formula for the difference of squares, you can rewrite this expression by expanding the parantheses

$\left(3 + \sqrt{7}\right) \left(3 - \sqrt{7}\right) = 3 \cdot 3 - \textcolor{red}{\cancel{\textcolor{b l a c k}{3 \cdot \sqrt{7}}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{3 \cdot \sqrt{7}}}} - \sqrt{7} \cdot \sqrt{7}$

Once again, the result will be

$3 \cdot 3 - \sqrt{7} \cdot \sqrt{7} = {3}^{2} - 7 = \textcolor{g r e e n}{2}$