To simplify this expression, we will first distribute the terms in the first set of parentheses:

(2√x + 1)(2√x - 1) = 4x - 1

Next, we will expand the second set of parentheses:

(2x + 1)² = (2x + 1)(2x + 1) = 4x² + 2x + 2x + 1 = 4x² + 4x + 1

Now, subtract the expanded second set of parentheses from the expanded first set of parentheses:

4x - 1 - (4x² + 4x + 1) = 4x - 1 - 4x² - 4x - 1 = -4x²

Therefore, the simplified expression is -4x².