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

##### 1 Answer

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 - 3x + 3x - 9 = x^2 - 9 # Note , however, that

# x^2 - 9 # is a 'difference of 2 squares'#and in general :

# x^2 - a^2 =(x - a )(x + a ) # so that

# x^2 - 9 = (x +3 )(x - 3 ) # Recognition of this fact would allow you to write

#x^2 - 9 # without having to use 'distributive law'