1. **State the problem:** Expand and simplify the expression $7a(3b - 4c) + 4a(3c - 2b)$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside. $$7a(3b - 4c) = 7a \times 3b - 7a \times 4c = 21ab - 28ac$$ $$4a(3c - 2b) = 4a \times 3c - 4a \times 2b = 12ac - 8ab$$ 3. **Rewrite the expression with expanded terms:** $$21ab - 28ac + 12ac - 8ab$$ 4. **Group like terms:** $$(21ab - 8ab) + (-28ac + 12ac)$$ 5. **Simplify each group:** $$21ab - 8ab = \cancel{21}ab - \cancel{8}ab = 13ab$$ $$-28ac + 12ac = -\cancel{28}ac + \cancel{12}ac = -16ac$$ 6. **Final simplified expression:** $$13ab - 16ac$$