1. **State the problem:** Factorize the expression $$4x^2 - \frac{1}{16}$$. 2. **Recognize the form:** This is a difference of squares, which follows the formula $$a^2 - b^2 = (a - b)(a + b)$$. 3. **Rewrite each term as a square:** $$4x^2 = (2x)^2$$ $$\frac{1}{16} = \left(\frac{1}{4}\right)^2$$ 4. **Apply the difference of squares formula:** $$4x^2 - \frac{1}{16} = (2x)^2 - \left(\frac{1}{4}\right)^2 = \left(2x - \frac{1}{4}\right)\left(2x + \frac{1}{4}\right)$$ 5. **Final answer:** $$\boxed{\left(2x - \frac{1}{4}\right)\left(2x + \frac{1}{4}\right)}$$