1. **State the problem:** Simplify the expression $ (a+3)(a+4) $. 2. **Use the distributive property (FOIL method):** Multiply each term in the first parenthesis by each term in the second parenthesis. 3. **Apply FOIL:** $$ (a+3)(a+4) = a \cdot a + a \cdot 4 + 3 \cdot a + 3 \cdot 4 $$ 4. **Calculate each product:** $$ = a^2 + 4a + 3a + 12 $$ 5. **Combine like terms:** $$ = a^2 + (4a + 3a) + 12 = a^2 + 7a + 12 $$ 6. **Final answer:** $$ (a+3)(a+4) = a^2 + 7a + 12 $$