Question

How do you factor completely `4x^2 - 9y^2`?

Answer 1

`color(blue)((2x+3y)(2x-3y)` is the factorised form of the expression

Explanation:

`4x^2-9y^2` can be also written as `(2x)^2-(3y)^2`

Now, as per identity:
`color(blue)(a^2-b^2=(a+b)(a-b)`

So , in case of our expression
`color(blue)(a=2x, b=3y`

`(2x)^2-(3y)^2=color(blue)((2x+3y)(2x-3y)`