1. The problem is to simplify the expression $4 - x^2$. 2. This is a difference of squares, which follows the formula $a^2 - b^2 = (a - b)(a + b)$. 3. Here, $4$ can be written as $2^2$, so the expression becomes $2^2 - x^2$. 4. Applying the difference of squares formula, we get: $$4 - x^2 = (2 - x)(2 + x)$$ 5. This is the fully factored form of the expression. 6. Therefore, the simplified form of $4 - x^2$ is $(2 - x)(2 + x)$.