# How do you evaluate (6+ \sqrt { 7} ) ( 4- \sqrt { 7} )?

Sep 18, 2017

You can use the F.O.I.L. method but that only applies to binomials (such as these). A more general method is to write each term of the first factor as a multiplier of the second factor.

#### Explanation:

Write each term of the first factor as a multiplier of the second factor:

$\left(6 + \sqrt{7}\right) \left(4 - \sqrt{7}\right) = 6 \left(4 - \sqrt{7}\right) + \sqrt{7} \left(4 - \sqrt{7}\right)$

Use the distributive property on both terms of the right side:

$\left(6 + \sqrt{7}\right) \left(4 - \sqrt{7}\right) = 24 - 6 \sqrt{7} + 4 \sqrt{7} - \sqrt{7} \sqrt{7}$

The last term becomes -7:

$\left(6 + \sqrt{7}\right) \left(4 - \sqrt{7}\right) = 24 - 6 \sqrt{7} + 4 \sqrt{7} - 7$

Combine like terms:

$\left(6 + \sqrt{7}\right) \left(4 - \sqrt{7}\right) = 17 - 2 \sqrt{7}$