Factorize 4p² - 9q².

We are tasked with factorizing the expression:

4p² - 9q²

This is a difference of squares, which follows the formula:

a² - b² = (a - b)(a + b)

To apply this, we first recognize the two squares in the given expression:

4p² is a perfect square because it can be written as (2p)².
9q² is also a perfect square because it can be written as (3q)².
Now, we can rewrite the expression as:

(2p)² - (3q)²

Using the difference of squares formula:

a² - b² = (a - b)(a + b)

we get:

(2p - 3q)(2p + 3q)

Thus, the factorized form of 4p² - 9q² is:

(2p - 3q)(2p + 3q)