1. **State the problem:** Factor completely the polynomial $$25x^2 - 9$$. 2. **Formula and rules:** Recognize this as a difference of squares: $$a^2 - b^2 = (a - b)(a + b)$$. 3. **Apply the formula:** Here, $$25x^2 = (5x)^2$$ and $$9 = 3^2$$. 4. **Factor:** $$25x^2 - 9 = (5x)^2 - 3^2 = (5x - 3)(5x + 3)$$. 5. **Final answer:** $$\boxed{(5x - 3)(5x + 3)}$$.