1. **Problem: Factor completely** the expression $25x^2 - 9$. 2. Recognize this as a difference of squares since $25x^2 = (5x)^2$ and $9 = 3^2$. 3. The formula for difference of squares is $$a^2 - b^2 = (a - b)(a + b)$$. 4. Applying the formula: $$25x^2 - 9 = (5x)^2 - 3^2 = (5x - 3)(5x + 3)$$. **Final answer:** $$25x^2 - 9 = (5x - 3)(5x + 3)$$