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, $a = x$ and $b = 2$ because $4 = 2^2$. 4. Applying the formula, we get: $$x^2 - 4 = (x - 2)(x + 2)$$ 5. This is the fully factored form of the expression. 6. So, the factorization of $x^2 - 4$ is $(x - 2)(x + 2)$.