1. The problem is to complete the factorization of the difference of squares expression $a^2 - b^2$. 2. The formula for the difference of squares is: $$a^2 - b^2 = (a + b)(a - b)$$ This means any expression in the form of one square minus another square can be factored into the product of the sum and difference of the square roots. 3. Applying this formula directly: $$a^2 - b^2 = (a + b)(a - b)$$ 4. This factorization works because when you multiply $(a + b)(a - b)$, you get: $$a^2 - ab + ab - b^2 = a^2 - b^2$$ The middle terms cancel out. 5. Therefore, the completed factorization is: $$a^2 - b^2 = (a + b)(a - b)$$