The problem asks us to factor the expression $9x^2 - 16y^4$.

1. Problem Description

The problem asks us to factor the expression $9x^2 - 16y^4$.

2. Solution Steps

We can recognize this expression as a difference of squares. The general formula for the difference of squares is:

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

In our case, we have $9x^2 - 16y^4$.

We can rewrite this as $(3x)^2 - (4y^2)^2$.

So, $a = 3x$ and $b = 4y^2$.

Applying the difference of squares formula, we get:

$(3x - 4y^2)(3x + 4y^2)$.

3. Final Answer

$(3x - 4y^2)(3x + 4y^2)$