1. **State the problem:** Simplify and factorize the expression $16x^2 - 100$. 2. **Recognize the form:** This is a difference of squares since $16x^2 = (4x)^2$ and $100 = 10^2$. 3. **Formula for difference of squares:** $$a^2 - b^2 = (a - b)(a + b)$$ 4. **Apply the formula:** Here, $a = 4x$ and $b = 10$, so $$16x^2 - 100 = (4x - 10)(4x + 10)$$ 5. **Check for further factorization:** Both factors can be simplified by factoring out 2: $$(4x - 10) = 2(2x - 5)$$ $$(4x + 10) = 2(2x + 5)$$ 6. **Combine the factors:** $$16x^2 - 100 = (4x - 10)(4x + 10) = 2(2x - 5) \times 2(2x + 5) = 4(2x - 5)(2x + 5)$$ **Final answer:** $$16x^2 - 100 = 4(2x - 5)(2x + 5)$$