1. **State the problem:** Simplify the algebraic expression $3r^2 - rs + 5s + r^2 - 2rs - 4s$. 2. **Combine like terms:** Group terms with $r^2$, terms with $rs$, and terms with $s$. 3. **Simplify each group:** - For $r^2$ terms: $3r^2 + r^2 = 4r^2$ - For $rs$ terms: $-rs - 2rs = -3rs$ - For $s$ terms: $5s - 4s = 1s = s$ 4. **Write the simplified expression:** $$4r^2 - 3rs + s$$ 5. **Explanation:** We combined coefficients of like terms by adding or subtracting them, which is a fundamental rule in algebra for simplifying expressions. The final simplified expression is $4r^2 - 3rs + s$.