# What is the standard form of  y= ( x + 3)(x - 3) ?

Jan 15, 2016

$y = {x}^{2} - 9$

#### Explanation:

Multiply out brackets (distributive law )

(x + 3 )(x - 3 ) = x(x - 3 ) + 3(x - 3 ) = ${x}^{2} - 3 x + 3 x - 9 = {x}^{2} - 9$

Note , however, that ${x}^{2} - 9$ is a 'difference of 2 squares'#

and in general : ${x}^{2} - {a}^{2} = \left(x - a\right) \left(x + a\right)$

so that ${x}^{2} - 9 = \left(x + 3\right) \left(x - 3\right)$

Recognition of this fact would allow you to write ${x}^{2} - 9$

without having to use 'distributive law'