Question

How do you factor `4x^2 - 81`?

Answer 1

`color(blue)((2x+9)(2x-9)`

Explanation:

`4x^2−81` can also be expressed as
`(2x)^2-9^2`

Now as per the property :
`color(blue)(a^2-b^2=(a+b)(a-b)` we can re write the expression.

`color(blue)((2x)^2-9^2= (2x+9)(2x-9)`
(here `a=2x, b=9)`

So the factorised form for the expression is
`color(blue)((2x+9)(2x-9)`