# How do you find the product (a-3)(a+3)?

Dec 26, 2016

$\left(a - 3\right) \left(a + 3\right) = \textcolor{g r e e n}{{a}^{2} - 9}$

#### Explanation:

Either remember the general case
$\textcolor{w h i t e}{\text{XXX}} \left(p - q\right) \left(p + q\right) = {p}^{2} - {q}^{2}$ (sometimes called "the difference of squares")

...or do the multiplication
$\left(a - 3\right) \left(a + 3\right)$
$\textcolor{w h i t e}{\text{XXX}} = \left(a - 3\right) a + \left(a - 3\right) 3$ (using the distributive property)

$\textcolor{w h i t e}{\text{XXX}} = \left({a}^{2} - 3 a\right) + \left(3 a - 9\right)$

$\textcolor{w h i t e}{\text{XXX}} = {a}^{2} - 9$

(could also be done using FOIL or tabular multiplcation)