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

Sep 5, 2016

$x - 7$

#### Explanation:

We have: $\left(\sqrt{x} - \sqrt{7}\right) \left(\sqrt{x} + \sqrt{7}\right)$

Let's expand the parentheses:

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

$= x + \sqrt{7 x} - \sqrt{7 x} - 7$

$= x - 7$

Sep 5, 2016

$x - 7$

#### Explanation:

Recall: difference of squares can be factored:

${x}^{2} - {y}^{2} = \left(x + y\right) \left(x - y\right)$

The reverse is also true, if 2 brackets are the same with different signs, we find that:

$\left(m + n\right) \left(m - n\right) = {m}^{2} - {n}^{2}$

This is what we have in this question,

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

=$x - 7$