Math worksheet for simplifying algebraic expressions by combining like terms.

Let's solve each expression by combining like terms. Like terms are terms that have the same variable(s) raised to the same power. We combine them by adding or subtracting their coefficients.

---

1. $ 4a + 3b - 2a + 5b $

- Combine $ 4a - 2a = 2a $
- Combine $ 3b + 5b = 8b $
- Answer: $ \boxed{2a + 8b} $

---

2. $ 4y - 2y + 3y - 6 $

- Combine $ 4y - 2y + 3y = (4 - 2 + 3)y = 5y $
- Constant: $ -6 $
- Answer: $ \boxed{5y - 6} $

---

3. $ 3p - 2q + 3p - 4q $

- Combine $ 3p + 3p = 6p $
- Combine $ -2q - 4q = -6q $
- Answer: $ \boxed{6p - 6q} $

---

4. $ 7c - 3d + 2c - 5d $

- Combine $ 7c + 2c = 9c $
- Combine $ -3d - 5d = -8d $
- Answer: $ \boxed{9c - 8d} $

---

5. $ 6m + 4n - 2m - 3n $

- Combine $ 6m - 2m = 4m $
- Combine $ 4n - 3n = 1n = n $
- Answer: $ \boxed{4m + n} $

---

6. $ 2a + 3b - 2a - 4b $

- Combine $ 2a - 2a = 0 $
- Combine $ 3b - 4b = -b $
- Answer: $ \boxed{-b} $

---

7. $ 4p - 3q + 2p + 5q - 3p $

- Combine $ 4p + 2p - 3p = 3p $
- Combine $ -3q + 5q = 2q $
- Answer: $ \boxed{3p + 2q} $

---

8. $ 9x - 2y + 3x - 2y + 5x - 3x $

- Combine $ 9x + 3x + 5x - 3x = (9+3+5-3)x = 14x $
- Combine $ -2y - 2y = -4y $
- Answer: $ \boxed{14x - 4y} $

---

9. $ 3x + 2y - z + 2x - y + 4z $

- Combine $ 3x + 2x = 5x $
- Combine $ 2y - y = y $
- Combine $ -z + 4z = 3z $
- Answer: $ \boxed{5x + y + 3z} $

---

10. $ 2a - b + 3c - 4a + 2b - 2c $

- Combine $ 2a - 4a = -2a $
- Combine $ -b + 2b = b $
- Combine $ 3c - 2c = c $
- Answer: $ \boxed{-2a + b + c} $

---

✔ Final Answers:

1. $ 2a + 8b $
2. $ 5y - 6 $
3. $ 6p - 6q $
4. $ 9c - 8d $
5. $ 4m + n $
6. $ -b $
7. $ 3p + 2q $
8. $ 14x - 4y $
9. $ 5x + y + 3z $
10. $ -2a + b + c $

---

Let me know if you'd like a step-by-step explanation for any one of them!