1. Given the equations: $$a^2 - b^2 = 32$$ $$a - b = 4$$ 2. Recognize that $a^2 - b^2$ can be factored as $(a - b)(a + b)$. 3. Substitute $a - b = 4$ into the factored form: $$ (a - b)(a + b) = 32 \implies 4 \times (a + b) = 32 $$ 4. Solve for $a + b$: $$ a + b = \frac{32}{4} = 8 $$ **Final answer:** $$ a + b = 8 $$