1. **State the problem:** Factorize the expression $$16x^2 - 100$$ fully. 2. **Simplify the expression:** Notice that both terms have a common factor of 4. $$16x^2 - 100 = 4(4x^2 - 25)$$ 3. **Recognize the difference of squares:** The expression inside the parentheses is a difference of squares since $$4x^2 = (2x)^2$$ and $$25 = 5^2$$. 4. **Apply the difference of squares formula:** $$a^2 - b^2 = (a - b)(a + b)$$ So, $$4x^2 - 25 = (2x - 5)(2x + 5)$$ 5. **Write the fully factorized form:** $$16x^2 - 100 = 4(2x - 5)(2x + 5)$$ 6. **Check the options:** The correct factorization matches option 3: $$4(2x - 5)(2x + 5)$$. **Final answer:** $$4(2x - 5)(2x + 5)$$