1. **State the problem:** Factorize the expression $x^2 - 1$. 2. **Recall the formula:** The expression $x^2 - 1$ is a difference of squares, which follows the rule: $$a^2 - b^2 = (a + b)(a - b)$$ where $a = x$ and $b = 1$. 3. **Apply the formula:** Using the difference of squares formula: $$x^2 - 1 = (x + 1)(x - 1)$$ 4. **Check the options:** - A) $(x + 3)(x - 3)$ corresponds to $x^2 - 9$. - B) $(x + 1)(x - 1)$ corresponds to $x^2 - 1$. - C) $(x + 4)(x - 4)$ corresponds to $x^2 - 16$. - D) $(x + 2)(x - 2)$ corresponds to $x^2 - 4$. 5. **Conclusion:** The correct factorization is option B: $(x + 1)(x - 1)$. **Final answer:** $(x + 1)(x - 1)$