1. **State the problem:** Factor the quadratic expression $x^2 - 4$. 2. **Recall the formula:** This expression is a difference of squares, which follows the rule: $$a^2 - b^2 = (a - b)(a + b)$$ 3. **Identify terms:** Here, $a = x$ and $b = 2$ because $4 = 2^2$. 4. **Apply the formula:** $$x^2 - 4 = (x - 2)(x + 2)$$ 5. **Explanation:** The difference of squares factors into the product of the sum and difference of the square roots of the terms. 6. **Final answer:** $$\boxed{(x - 2)(x + 2)}$$