1. **State the problem:** Simplify the expression $e^2 + e^1$. 2. **Recall the exponential notation:** $e^n$ means $e$ raised to the power of $n$. 3. **Rewrite the expression:** $e^2 + e^1 = e^2 + e$. 4. **Factor out the common term:** Both terms have a factor of $e$, so we can write: $$e^2 + e = e \cdot e + e = e(e + 1)$$ 5. **Final simplified form:** $$e(e + 1)$$ This is the simplest factorized form of the expression.