1. **State the problem:** Simplify the expression $$3(n + 3mn) - 5n(2m - 1)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside. $$3(n + 3mn) = 3 \times n + 3 \times 3mn = 3n + 9mn$$ $$-5n(2m - 1) = -5n \times 2m + (-5n) \times (-1) = -10mn + 5n$$ 3. **Rewrite the expression with distributed terms:** $$3n + 9mn - 10mn + 5n$$ 4. **Combine like terms:** - Combine terms with $n$: $3n + 5n = 8n$ - Combine terms with $mn$: $9mn - 10mn = -1mn = -mn$ 5. **Final simplified expression:** $$8n - mn$$ This is the simplified form of the original expression.