To simplify the expression (4x + 9y)^2 - 4x^2, we can expand the square of the binomial (4x + 9y)^2 and then subtract 4x^2.

Expanding (4x + 9y)^2:
(4x + 9y)^2 = (4x + 9y)(4x + 9y)
Using the FOIL method:
= (4x)(4x) + (4x)(9y) + (9y)(4x) + (9y)(9y)
= 16x^2 + 36xy + 36xy + 81y^2
= 16x^2 + 72xy + 81y^2

Now, subtracting 4x^2:
(16x^2 + 72xy + 81y^2) - 4x^2
= 16x^2 - 4x^2 + 72xy + 81y^2
= 12x^2 + 72xy + 81y^2

Therefore, the simplified expression is 12x^2 + 72xy + 81y^2.