# How do you multiply (sqrtt-y) (sqrtt+y) ?

Sep 13, 2015

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

#### Explanation:

In general we have a standard formula called the difference of squares:
$\textcolor{w h i t e}{\text{XX}} \left({a}^{2} - {b}^{2}\right) = \left(a - b\right) \left(a + b\right)$

This can be written in reverse as
$\textcolor{w h i t e}{\text{XX}} \left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$

Substituting
color(white)("XX")sqrt(t) " for "a
and
color(white)("XX")y " for " b

we have
$\textcolor{w h i t e}{\text{XX}} \left(\sqrt{t} - y\right) \left(\sqrt{t} + y\right)$

$\textcolor{w h i t e}{\text{XXX}} = {\left(\sqrt{t}\right)}^{2} - {y}^{2}$

$\textcolor{w h i t e}{\text{XXX}} = t - {y}^{2}$