1. **State the problem:** Simplify the expression $4n + 1 + 4n$. 2. **Combine like terms:** The terms $4n$ and $4n$ are like terms because they both contain the variable $n$. 3. **Add the coefficients of like terms:** $$4n + 4n = (4 + 4)n = 8n$$ 4. **Rewrite the expression:** $$8n + 1$$ 5. **Final answer:** The simplified expression is $8n + 1$. This means you add the coefficients of the terms with $n$ and keep the constant separate.