1. The problem is to factor the expression $x^2 - 4$. 2. Recognize that this is a difference of squares, which follows the formula $$a^2 - b^2 = (a - b)(a + b)$$. 3. Here, $x^2$ is $(x)^2$ and $4$ is $(2)^2$. 4. Applying the difference of squares formula, we get: $$x^2 - 4 = (x - 2)(x + 2)$$ 5. This is the fully factored form of the expression. 6. Therefore, the factorization of $x^2 - 4$ is $$(x - 2)(x + 2)$$.