# How do you simplify (3 – 2sqrt7)(3 + 2sqrt7)?

Jan 26, 2017

$\left(3 - 2 \sqrt{7}\right) \left(3 + 2 \sqrt{7}\right) = - 19$

#### Explanation:

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

This is a difference of squares problem, ${a}^{2} - {b}^{2}$, where $a = 3$, and $b = 2 \sqrt{7}$.

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

Simplify.

$9 - {\left(2 \sqrt{7}\right)}^{2}$

Apply multiplication distributive property, ${\left(x y\right)}^{m} = {x}^{m} {y}^{m}$.

$9 - {2}^{2} {\sqrt{7}}^{2}$

Simplify.

$9 - 4 \times {\left(\sqrt{7}\right)}^{2}$

Apply square root rule, ${\left(\sqrt{x}\right)}^{2} = x$.

Simplify.

$9 - 4 \times 7$

Simplify. Apply order of operations and multiply $4 \times 7$ first.

$9 - 28$

Simplify.

$- 19$