Question

How do you factor `4b^2 - 9`?

Answer 1

`4b^2 - 9 = (2b + 3)(2b-3)`

Explanation:

The difference of squares formula states that
`a^2 - b^2 = (a+b)(a-b)`
(this may be easily verified by expanding the right hand side of the equation)

`4b^2 = (2b)^2`
`9 = 3^2`

Thus, by the difference of squares formula:

`4b^2 - 9 = (2b)^2 - 3^2 = (2b + 3)(2b-3)`