1. **Problem Statement:** Factorize the expression $b^2 - 4$. 2. **Formula Used:** This is a difference of squares, which follows the rule: $$a^2 - b^2 = (a - b)(a + b)$$ 3. **Apply the Rule:** Here, $b^2$ is $a^2$ and $4$ is $2^2$. So, $$b^2 - 4 = b^2 - 2^2 = (b - 2)(b + 2)$$ 4. **Check the Options:** - A) $(b - 1)(b + 1)$ corresponds to $b^2 - 1$ - B) $(b - 4)(b + 4)$ corresponds to $b^2 - 16$ - C) $(b - 3)(b + 3)$ corresponds to $b^2 - 9$ - D) $(b - 2)(b + 2)$ corresponds to $b^2 - 4$ 5. **Final Answer:** The correct factorization is option D: $(b - 2)(b + 2)$. This factorization is useful because it breaks down a quadratic expression into two binomials, making it easier to solve or simplify further.