# How do you evaluate (\sqrt { p } - a ) ( \sqrt { p } + a )?

##### 1 Answer
Apr 4, 2018

$p - {a}^{2}$

#### Explanation:

$\left(\sqrt{p} - a\right) \left(\sqrt{p} + a\right)$

Let's write out what each of them multiplies to in order to make it clearer:

$\sqrt{p} \cdot \sqrt{p} = p$

$\sqrt{p} \cdot a = a \sqrt{p}$

$- a \cdot \sqrt{p} = - a \sqrt{p}$

$- a \cdot a = - {a}^{2}$

When we combine them all together we get:
$p + a \sqrt{p} - a \sqrt{p} - {a}^{2}$

We can still simplify this as $a \sqrt{p} \mathmr{and} - a \sqrt{p}$ are in common. So the final answer is:
$p - {a}^{2}$

Hope this helps!