# How do you simplify (9 + 2sqrt3)(9 - 2sqrt3)?

Apr 6, 2018

You can use the identity $\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$. A quick proof of this:

$\left(a - b\right) \left(a + b\right) = a a + \setminus \cancel{+ a b - b a} - b \setminus b = {a}^{2} - {b}^{2}$

In your specific case, $\left(9 + 2 \setminus \sqrt{3}\right) \left(9 - 2 \setminus \sqrt{3}\right) = {9}^{2} - {\left(2 \setminus \sqrt{3}\right)}^{2} = 81 - 12 = 69$.

Apr 6, 2018

$69$

#### Explanation:

We will use this formula: $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$.
Let,
$a = 9$
$b = 2 \sqrt{3}$

Now put these values in the formula:
$\left(9 + 2 \sqrt{3}\right) \left(9 - 2 \sqrt{3}\right)$

${9}^{2} - {\left(2 \sqrt{3}\right)}^{2}$

$81 - 4 \cdot 3$

$81 - 12$

and you get $69$.