Adding and Subtracting Polynomials worksheet with 30 practice problems for simplifying algebraic expressions.

Problem: Simplify each polynomial expression by adding or subtracting like terms.

#### Step-by-Step Solution:

We will simplify each expression by combining like terms. Like terms are terms that have the same variable(s) raised to the same power(s).

---

1. \( (-2x + 6) + (4x - 4) \)

- Combine the \( x \)-terms: \( -2x + 4x = 2x \)
- Combine the constant terms: \( 6 - 4 = 2 \)

Simplified Expression: \( 2x + 2 \)

---

2. \( (-4x^2 + 7x) - (4x^2 + 5x) \)

- Distribute the negative sign: \( -4x^2 + 7x - 4x^2 - 5x \)
- Combine the \( x^2 \)-terms: \( -4x^2 - 4x^2 = -8x^2 \)
- Combine the \( x \)-terms: \( 7x - 5x = 2x \)

Simplified Expression: \( -8x^2 + 2x \)

---

3. \( (-2x^2 + 7x) - (2x^2 + 5x) \)

- Distribute the negative sign: \( -2x^2 + 7x - 2x^2 - 5x \)
- Combine the \( x^2 \)-terms: \( -2x^2 - 2x^2 = -4x^2 \)
- Combine the \( x \)-terms: \( 7x - 5x = 2x \)

Simplified Expression: \( -4x^2 + 2x \)

---

4. \( (-4x^2 + 3x) + (2x^2 - 2x) \)

- Combine the \( x^2 \)-terms: \( -4x^2 + 2x^2 = -2x^2 \)
- Combine the \( x \)-terms: \( 3x - 2x = x \)

Simplified Expression: \( -2x^2 + x \)

---

5. \( (5x + 9) - (4x + 7) \)

- Distribute the negative sign: \( 5x + 9 - 4x - 7 \)
- Combine the \( x \)-terms: \( 5x - 4x = x \)
- Combine the constant terms: \( 9 - 7 = 2 \)

Simplified Expression: \( x + 2 \)

---

6. \( (10x + 6) - (5x + 2) \)

- Distribute the negative sign: \( 10x + 6 - 5x - 2 \)
- Combine the \( x \)-terms: \( 10x - 5x = 5x \)
- Combine the constant terms: \( 6 - 2 = 4 \)

Simplified Expression: \( 5x + 4 \)

---

7. \( (-3x^2 + 9x) - (7x^2 + 7x) \)

- Distribute the negative sign: \( -3x^2 + 9x - 7x^2 - 7x \)
- Combine the \( x^2 \)-terms: \( -3x^2 - 7x^2 = -10x^2 \)
- Combine the \( x \)-terms: \( 9x - 7x = 2x \)

Simplified Expression: \( -10x^2 + 2x \)

---

8. \( (-10x^2 + 8x) + (3x^2 - 6x) \)

- Combine the \( x^2 \)-terms: \( -10x^2 + 3x^2 = -7x^2 \)
- Combine the \( x \)-terms: \( 8x - 6x = 2x \)

Simplified Expression: \( -7x^2 + 2x \)

---

9. \( (9x + 4) + (7x - 2) \)

- Combine the \( x \)-terms: \( 9x + 7x = 16x \)
- Combine the constant terms: \( 4 - 2 = 2 \)

Simplified Expression: \( 16x + 2 \)

---

10. \( (5x + 8) + (4x - 6) \)

- Combine the \( x \)-terms: \( 5x + 4x = 9x \)
- Combine the constant terms: \( 8 - 6 = 2 \)

Simplified Expression: \( 9x + 2 \)

---

11. \( (2x^2 + 7x) - (2x^2 + 3x) \)

- Distribute the negative sign: \( 2x^2 + 7x - 2x^2 - 3x \)
- Combine the \( x^2 \)-terms: \( 2x^2 - 2x^2 = 0 \)
- Combine the \( x \)-terms: \( 7x - 3x = 4x \)

Simplified Expression: \( 4x \)

---

12. \( (-10x + 4) + (7x - 3) \)

- Combine the \( x \)-terms: \( -10x + 7x = -3x \)
- Combine the constant terms: \( 4 - 3 = 1 \)

Simplified Expression: \( -3x + 1 \)

---

13. \( (-4x + 6) + (2x - 4) \)

- Combine the \( x \)-terms: \( -4x + 2x = -2x \)
- Combine the constant terms: \( 6 - 4 = 2 \)

Simplified Expression: \( -2x + 2 \)

---

14. \( (8x + 8) + (3x - 6) \)

- Combine the \( x \)-terms: \( 8x + 3x = 11x \)
- Combine the constant terms: \( 8 - 6 = 2 \)

Simplified Expression: \( 11x + 2 \)

---

15. \( (10x^2 + 5x) - (5x^2 + 4x) \)

- Distribute the negative sign: \( 10x^2 + 5x - 5x^2 - 4x \)
- Combine the \( x^2 \)-terms: \( 10x^2 - 5x^2 = 5x^2 \)
- Combine the \( x \)-terms: \( 5x - 4x = x \)

Simplified Expression: \( 5x^2 + x \)

---

16. \( (-9x + 5) - (2x + 3) \)

- Distribute the negative sign: \( -9x + 5 - 2x - 3 \)
- Combine the \( x \)-terms: \( -9x - 2x = -11x \)
- Combine the constant terms: \( 5 - 3 = 2 \)

Simplified Expression: \( -11x + 2 \)

---

17. \( (8x + 9) - (6x + 7) \)

- Distribute the negative sign: \( 8x + 9 - 6x - 7 \)
- Combine the \( x \)-terms: \( 8x - 6x = 2x \)
- Combine the constant terms: \( 9 - 7 = 2 \)

Simplified Expression: \( 2x + 2 \)

---

18. \( (-8x^2 + 4x) - (6x^2 + 2x) \)

- Distribute the negative sign: \( -8x^2 + 4x - 6x^2 - 2x \)
- Combine the \( x^2 \)-terms: \( -8x^2 - 6x^2 = -14x^2 \)
- Combine the \( x \)-terms: \( 4x - 2x = 2x \)

Simplified Expression: \( -14x^2 + 2x \)

---

19. \( (-7x + 9) - (6x + 7) \)

- Distribute the negative sign: \( -7x + 9 - 6x - 7 \)
- Combine the \( x \)-terms: \( -7x - 6x = -13x \)
- Combine the constant terms: \( 9 - 7 = 2 \)

Simplified Expression: \( -13x + 2 \)

---

20. \( (-4x + 9) - (5x + 7) \)

- Distribute the negative sign: \( -4x + 9 - 5x - 7 \)
- Combine the \( x \)-terms: \( -4x - 5x = -9x \)
- Combine the constant terms: \( 9 - 7 = 2 \)

Simplified Expression: \( -9x + 2 \)

---

21. \( (3x + 4) + (7x - 3) \)

- Combine the \( x \)-terms: \( 3x + 7x = 10x \)
- Combine the constant terms: \( 4 - 3 = 1 \)

Simplified Expression: \( 10x + 1 \)

---

22. \( (1x + 9) + (3x - 7) \)

- Combine the \( x \)-terms: \( 1x + 3x = 4x \)
- Combine the constant terms: \( 9 - 7 = 2 \)

Simplified Expression: \( 4x + 2 \)

---

23. \( (3x + 5) - (5x + 4) \)

- Distribute the negative sign: \( 3x + 5 - 5x - 4 \)
- Combine the \( x \)-terms: \( 3x - 5x = -2x \)
- Combine the constant terms: \( 5 - 4 = 1 \)

Simplified Expression: \( -2x + 1 \)

---

24. \( (6x + 3) + (2x - 2) \)

- Combine the \( x \)-terms: \( 6x + 2x = 8x \)
- Combine the constant terms: \( 3 - 2 = 1 \)

Simplified Expression: \( 8x + 1 \)

---

25. \( (-5x + 6) - (2x + 5) \)

- Distribute the negative sign: \( -5x + 6 - 2x - 5 \)
- Combine the \( x \)-terms: \( -5x - 2x = -7x \)
- Combine the constant terms: \( 6 - 5 = 1 \)

Simplified Expression: \( -7x + 1 \)

---

26. \( (-2x + 6) - (4x + 5) \)

- Distribute the negative sign: \( -2x + 6 - 4x - 5 \)
- Combine the \( x \)-terms: \( -2x - 4x = -6x \)
- Combine the constant terms: \( 6 - 5 = 1 \)

Simplified Expression: \( -6x + 1 \)

---

27. \( (-9x^2 + 9x) + (3x^2 - 7x) \)

- Combine the \( x^2 \)-terms: \( -9x^2 + 3x^2 = -6x^2 \)
- Combine the \( x \)-terms: \( 9x - 7x = 2x \)

Simplified Expression: \( -6x^2 + 2x \)

---

28. \( (-10x + 7) - (7x + 5) \)

- Distribute the negative sign: \( -10x + 7 - 7x - 5 \)
- Combine the \( x \)-terms: \( -10x - 7x = -17x \)
- Combine the constant terms: \( 7 - 5 = 2 \)

Simplified Expression: \( -17x + 2 \)

---

29. \( (4x^2 + 9x) - (7x^2 + 7x) \)

- Distribute the negative sign: \( 4x^2 + 9x - 7x^2 - 7x \)
- Combine the \( x^2 \)-terms: \( 4x^2 - 7x^2 = -3x^2 \)
- Combine the \( x \)-terms: \( 9x - 7x = 2x \)

Simplified Expression: \( -3x^2 + 2x \)

---

30. \( (6x + 6) - (5x + 3) \)

- Distribute the negative sign: \( 6x + 6 - 5x - 3 \)
- Combine the \( x \)-terms: \( 6x - 5x = x \)
- Combine the constant terms: \( 6 - 3 = 3 \)

Simplified Expression: \( x + 3 \)

---

Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & 2x + 2 \\
2. & -8x^2 + 2x \\
3. & -4x^2 + 2x \\
4. & -2x^2 + x \\
5. & x + 2 \\
6. & 5x + 4 \\
7. & -10x^2 + 2x \\
8. & -7x^2 + 2x \\
9. & 16x + 2 \\
10. & 9x + 2 \\
11. & 4x \\
12. & -3x + 1 \\
13. & -2x + 2 \\
14. & 11x + 2 \\
15. & 5x^2 + x \\
16. & -11x + 2 \\
17. & 2x + 2 \\
18. & -14x^2 + 2x \\
19. & -13x + 2 \\
20. & -9x + 2 \\
21. & 10x + 1 \\
22. & 4x + 2 \\
23. & -2x + 1 \\
24. & 8x + 1 \\
25. & -7x + 1 \\
26. & -6x + 1 \\
27. & -6x^2 + 2x \\
28. & -17x + 2 \\
29. & -3x^2 + 2x \\
30. & x + 3 \\
\end{array}
}
\]