1. The problem states the identity $a^2 - b^2 = (a - b)(a + b)$. 2. This is a difference of squares formula, which says that the difference between two squares can be factored into the product of the sum and difference of the two terms. 3. To verify, expand the right side: $$ (a - b)(a + b) = a \cdot a + a \cdot b - b \cdot a - b \cdot b = a^2 + ab - ab - b^2 = a^2 - b^2 $$ 4. The middle terms $+ab$ and $-ab$ cancel out, leaving $a^2 - b^2$. 5. This formula is useful for factoring expressions and simplifying algebraic expressions. Final answer: $$a^2 - b^2 = (a - b)(a + b)$$