1. **State the problem:** Simplify the algebraic expressions: a) $4a + 7b + 5a - b$ b) $6c + 4d - c - 7d$ 2. **Formula and rules:** To simplify algebraic expressions, combine like terms. Like terms have the same variable raised to the same power. 3. **Simplify part (a):** Combine the $a$ terms: $4a + 5a = 9a$ Combine the $b$ terms: $7b - b = 6b$ So, $4a + 7b + 5a - b = 9a + 6b$ 4. **Simplify part (b):** Combine the $c$ terms: $6c - c = 5c$ Combine the $d$ terms: $4d - 7d = -3d$ So, $6c + 4d - c - 7d = 5c - 3d$ **Final answers:** a) $9a + 6b$ b) $5c - 3d$