Question

How do you multiply `(2x + 3) (2x - 3)`?

Answer 1

`4x^2-9`

Explanation:

Split one of the brackets:
`(2x+3)(2x-3)=2x(2x-3)+3(2x-3)`

Split the remaining bracket:
`2x(2x)+2x(-3)+3(2x)+3(-3)=4x^2-6x+6x-9`

Combined the expanded terms:
`4x^2-9`

Answer 2

Alternatively, use the FOIL mnemonic to pick out pairs of terms to multiply from the two binomials...

Explanation:

`(2x+3)(2x-3)`

`=underbrace(2x*2x)_color(blue)("First")+underbrace(2x*-3)_color(blue)("Outside")+underbrace(3*2x)_color(blue)("Inside")+underbrace(3*-3)_color(blue)("Last")`

`=4x^2-cancel(6x)+cancel(6x)-9`

`=4x^2-9`

Or:
You could use the 'special product' of the form:
`(a+b)(a-b)=a^2-b^2->`
`(2x+3)(2x-3)=(2x)^2-3^2=4x^2-9`