1. **State the problem:** Simplify the expression $4(8 + 4a) - 8 + 7a$. 2. **Apply the distributive property:** Multiply $4$ by each term inside the parentheses: $$4 \times 8 + 4 \times 4a = 32 + 16a$$ So the expression becomes: $$32 + 16a - 8 + 7a$$ 3. **Combine like terms:** Group constants and terms with $a$: Constants: $32 - 8$ Terms with $a$: $16a + 7a$ 4. **Simplify constants:** $$32 - 8 = \cancel{32} - \cancel{8} = 24$$ 5. **Simplify terms with $a$:** $$16a + 7a = 23a$$ 6. **Write the simplified expression:** $$24 + 23a$$ **Final answer:** $24 + 23a$