1. **State the problem:** Simplify the expression $1 - a^2$. 2. **Recall the formula:** The expression $1 - a^2$ is a difference of squares, which can be factored using the identity: $$x^2 - y^2 = (x - y)(x + y)$$ Here, $x = 1$ and $y = a$. 3. **Apply the formula:** $$1 - a^2 = (1 - a)(1 + a)$$ 4. **Explanation:** The difference of squares formula allows us to rewrite the subtraction of two squares as the product of the sum and difference of their roots. 5. **Final answer:** $$1 - a^2 = (1 - a)(1 + a)$$