The problem requires us to factor the expression $4 - 81x^2y^2$ using the difference of two squares formula.

1. Problem Description

The problem requires us to factor the expression $4 - 81x^2y^2$ using the difference of two squares formula.

2. Solution Steps

The difference of two squares formula is:

$a^2 - b^2 = (a - b)(a + b)$

We need to express the given expression $4 - 81x^2y^2$ in the form $a^2 - b^2$.

We can rewrite $4$ as $2^2$ and $81x^2y^2$ as $(9xy)^2$.

So, we have $4 - 81x^2y^2 = 2^2 - (9xy)^2$.

Now, we can apply the difference of two squares formula:

$2^2 - (9xy)^2 = (2 - 9xy)(2 + 9xy)$

3. Final Answer

$(2 - 9xy)(2 + 9xy)$