Question

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

Answer 1

`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'