Math worksheet for simplifying polynomial expressions, including addition and subtraction problems.

Problem: Simplify each polynomial expression.

We will simplify each expression step by step, combining like terms. Let's go through them one by one.

---

#### 1. \( (-4x^3y^3 - 6x^2y^2) - (2x^3y^3 - 7x^2y^2) \)

- Distribute the negative sign:
\[
-4x^3y^3 - 6x^2y^2 - 2x^3y^3 + 7x^2y^2
\]

- Combine like terms:
\[
(-4x^3y^3 - 2x^3y^3) + (-6x^2y^2 + 7x^2y^2)
\]
\[
= -6x^3y^3 + x^2y^2
\]

- Answer: \(\boxed{-6x^3y^3 + x^2y^2}\)

---

#### 2. \( (7y + 3x^2y^3) + (6x^2 + 4x^2y^3) \)

- Combine like terms:
\[
7y + 3x^2y^3 + 6x^2 + 4x^2y^3
\]
\[
= 7y + (3x^2y^3 + 4x^2y^3) + 6x^2
\]
\[
= 7y + 7x^2y^3 + 6x^2
\]

- Answer: \(\boxed{7y + 7x^2y^3 + 6x^2}\)

---

#### 3. \( (-5x^2y - 4x^3) - (4x^3 + 6x^2y) \)

- Distribute the negative sign:
\[
-5x^2y - 4x^3 - 4x^3 - 6x^2y
\]

- Combine like terms:
\[
(-5x^2y - 6x^2y) + (-4x^3 - 4x^3)
\]
\[
= -11x^2y - 8x^3
\]

- Answer: \(\boxed{-11x^2y - 8x^3}\)

---

#### 4. \( (6x^2y^2 - 6x^3y) + (4x^3y - 4x^2y^2) \)

- Combine like terms:
\[
6x^2y^2 - 6x^3y + 4x^3y - 4x^2y^2
\]
\[
= (6x^2y^2 - 4x^2y^2) + (-6x^3y + 4x^3y)
\]
\[
= 2x^2y^2 - 2x^3y
\]

- Answer: \(\boxed{2x^2y^2 - 2x^3y}\)

---

#### 5. \( (5b^2 - 1) - (-8b - 7) \)

- Distribute the negative sign:
\[
5b^2 - 1 + 8b + 7
\]

- Combine like terms:
\[
5b^2 + 8b + (-1 + 7)
\]
\[
= 5b^2 + 8b + 6
\]

- Answer: \(\boxed{5b^2 + 8b + 6}\)

---

#### 6. \( (-mn^3 + 2m^3) - (5mn^3 - 2m^2n^2) \)

- Distribute the negative sign:
\[
-mn^3 + 2m^3 - 5mn^3 + 2m^2n^2
\]

- Combine like terms:
\[
(-mn^3 - 5mn^3) + 2m^3 + 2m^2n^2
\]
\[
= -6mn^3 + 2m^3 + 2m^2n^2
\]

- Answer: \(\boxed{-6mn^3 + 2m^3 + 2m^2n^2}\)

---

#### 7. \( (-7xy^2 - 8) + (7 + 8x^3y^3) \)

- Combine like terms:
\[
-7xy^2 - 8 + 7 + 8x^3y^3
\]
\[
= 8x^3y^3 - 7xy^2 + (-8 + 7)
\]
\[
= 8x^3y^3 - 7xy^2 - 1
\]

- Answer: \(\boxed{8x^3y^3 - 7xy^2 - 1}\)

---

#### 8. \( (4x^2y^3 - 5x^2) + (-4x^2y^3 - 4x^2) \)

- Combine like terms:
\[
4x^2y^3 - 5x^2 - 4x^2y^3 - 4x^2
\]
\[
= (4x^2y^3 - 4x^2y^3) + (-5x^2 - 4x^2)
\]
\[
= 0 + (-9x^2)
\]
\[
= -9x^2
\]

- Answer: \(\boxed{-9x^2}\)

---

#### 9. \( (4m^2 - 6m^3n^3) - (-8m^3n^3 + 5m^2) \)

- Distribute the negative sign:
\[
4m^2 - 6m^3n^3 + 8m^3n^3 - 5m^2
\]

- Combine like terms:
\[
(4m^2 - 5m^2) + (-6m^3n^3 + 8m^3n^3)
\]
\[
= -m^2 + 2m^3n^3
\]

- Answer: \(\boxed{-m^2 + 2m^3n^3}\)

---

#### 10. \( (-uv - 7u^2v^2) + (-2uv + 4u^2v^2) \)

- Combine like terms:
\[
-uv - 7u^2v^2 - 2uv + 4u^2v^2
\]
\[
= (-uv - 2uv) + (-7u^2v^2 + 4u^2v^2)
\]
\[
= -3uv - 3u^2v^2
\]

- Answer: \(\boxed{-3uv - 3u^2v^2}\)

---

#### 11. \( (6x - 6y) - (2x + 8y) \)

- Distribute the negative sign:
\[
6x - 6y - 2x - 8y
\]

- Combine like terms:
\[
(6x - 2x) + (-6y - 8y)
\]
\[
= 4x - 14y
\]

- Answer: \(\boxed{4x - 14y}\)

---

#### 12. \( (3v^3 - u^3v) + (7v^3 + u^3v) \)

- Combine like terms:
\[
3v^3 - u^3v + 7v^3 + u^3v
\]
\[
= (3v^3 + 7v^3) + (-u^3v + u^3v)
\]
\[
= 10v^3 + 0
\]
\[
= 10v^3
\]

- Answer: \(\boxed{10v^3}\)

---

#### 13. \( (-5x^2y + 3x^3y) - (-5x^3y + x^2y) \)

- Distribute the negative sign:
\[
-5x^2y + 3x^3y + 5x^3y - x^2y
\]

- Combine like terms:
\[
(-5x^2y - x^2y) + (3x^3y + 5x^3y)
\]
\[
= -6x^2y + 8x^3y
\]

- Answer: \(\boxed{-6x^2y + 8x^3y}\)

---

#### 14. \( (-4a^2b - a) - (5a - 3a^2b) \)

- Distribute the negative sign:
\[
-4a^2b - a - 5a + 3a^2b
\]

- Combine like terms:
\[
(-4a^2b + 3a^2b) + (-a - 5a)
\]
\[
= -a^2b - 6a
\]

- Answer: \(\boxed{-a^2b - 6a}\)

---

#### 15. \( (-7xy - 5y^2) + (5y^2 - 2xy) \)

- Combine like terms:
\[
-7xy - 5y^2 + 5y^2 - 2xy
\]
\[
= (-7xy - 2xy) + (-5y^2 + 5y^2)
\]
\[
= -9xy + 0
\]
\[
= -9xy
\]

- Answer: \(\boxed{-9xy}\)

---

#### 16. \( (7m^3n - mn^2) - (-7m^3n + 8mn^2) \)

- Distribute the negative sign:
\[
7m^3n - mn^2 + 7m^3n - 8mn^2
\]

- Combine like terms:
\[
(7m^3n + 7m^3n) + (-mn^2 - 8mn^2)
\]
\[
= 14m^3n - 9mn^2
\]

- Answer: \(\boxed{14m^3n - 9mn^2}\)

---

#### 17. \( (4x - 5y^2) + (-x + y^2) \)

- Combine like terms:
\[
4x - 5y^2 - x + y^2
\]
\[
= (4x - x) + (-5y^2 + y^2)
\]
\[
= 3x - 4y^2
\]

- Answer: \(\boxed{3x - 4y^2}\)

---

#### 18. \( (8m^3n^2 + 4n^2) - (6n^2 - 6m^3n^2) \)

- Distribute the negative sign:
\[
8m^3n^2 + 4n^2 - 6n^2 + 6m^3n^2
\]

- Combine like terms:
\[
(8m^3n^2 + 6m^3n^2) + (4n^2 - 6n^2)
\]
\[
= 14m^3n^2 - 2n^2
\]

- Answer: \(\boxed{14m^3n^2 - 2n^2}\)

---

#### 19. \( (-3u^3v^2 - 5u^3v) + (-8u^3v^2 + 4u^3v) \)

- Combine like terms:
\[
-3u^3v^2 - 5u^3v - 8u^3v^2 + 4u^3v
\]
\[
= (-3u^3v^2 - 8u^3v^2) + (-5u^3v + 4u^3v)
\]
\[
= -11u^3v^2 - u^3v
\]

- Answer: \(\boxed{-11u^3v^2 - u^3v}\)

---

#### 20. \( (7v^2 - 5uv^2) - (2uv^2 + 7v^2) \)

- Distribute the negative sign:
\[
7v^2 - 5uv^2 - 2uv^2 - 7v^2
\]

- Combine like terms:
\[
(7v^2 - 7v^2) + (-5uv^2 - 2uv^2)
\]
\[
= 0 - 7uv^2
\]
\[
= -7uv^2
\]

- Answer: \(\boxed{-7uv^2}\)

---

#### 21. \( (-6xy^3 + 2x^2y^2) + (-3xy^3 + 7x^2y^2) \)

- Combine like terms:
\[
-6xy^3 + 2x^2y^2 - 3xy^3 + 7x^2y^2
\]
\[
= (-6xy^3 - 3xy^3) + (2x^2y^2 + 7x^2y^2)
\]
\[
= -9xy^3 + 9x^2y^2
\]

- Answer: \(\boxed{-9xy^3 + 9x^2y^2}\)

---

#### 22. \( (-4xy^3 + 6x^3) - (8x^3 - 3xy^3) \)

- Distribute the negative sign:
\[
-4xy^3 + 6x^3 - 8x^3 + 3xy^3
\]

- Combine like terms:
\[
(-4xy^3 + 3xy^3) + (6x^3 - 8x^3)
\]
\[
= -xy^3 - 2x^3
\]

- Answer: \(\boxed{-xy^3 - 2x^3}\)

---

#### 23. \( (-7b^3 - 4a^2b^3) - (-5b^3 - 7a^2b^3) \)

- Distribute the negative sign:
\[
-7b^3 - 4a^2b^3 + 5b^3 + 7a^2b^3
\]

- Combine like terms:
\[
(-7b^3 + 5b^3) + (-4a^2b^3 + 7a^2b^3)
\]
\[
= -2b^3 + 3a^2b^3
\]

- Answer: \(\boxed{-2b^3 + 3a^2b^3}\)

---

#### 24. \( (7x^3y^3 + y^2) - (3y^2 - x^3y^3) \)

- Distribute the negative sign:
\[
7x^3y^3 + y^2 - 3y^2 + x^3y^3
\]

- Combine like terms:
\[
(7x^3y^3 + x^3y^3) + (y^2 - 3y^2)
\]
\[
= 8x^3y^3 - 2y^2
\]

- Answer: \(\boxed{8x^3y^3 - 2y^2}\)

---

#### 25. \( (3m^3 - 4m^3n^3) - (5m^3n^3 - 4m^3) \)

- Distribute the negative sign:
\[
3m^3 - 4m^3n^3 - 5m^3n^3 + 4m^3
\]

- Combine like terms:
\[
(3m^3 + 4m^3) + (-4m^3n^3 - 5m^3n^3)
\]
\[
= 7m^3 - 9m^3n^3
\]

- Answer: \(\boxed{7m^3 - 9m^3n^3}\)

---

#### 26. \( (7x + 7x^3y^3) + (-7x^3y^3 - 7x) - (6x^3y^2 - 2x) \)

- Combine all terms:
\[
7x + 7x^3y^3 - 7x^3y^3 - 7x - 6x^3y^2 + 2x
\]

- Group like terms:
\[
(7x - 7x + 2x) + (7x^3y^3 - 7x^3y^3) - 6x^3y^2
\]
\[
= 2x + 0 - 6x^3y^2
\]
\[
= 2x - 6x^3y^2
\]

- Answer: \(\boxed{2x - 6x^3y^2}\)

---

#### 27. \( (-2u + 5v) - (-2v + 2u) - (7u - 7uv) \)

- Distribute the negative signs:
\[
-2u + 5v + 2v - 2u - 7u + 7uv
\]

- Combine like terms:
\[
(-2u - 2u - 7u) + (5v + 2v) + 7uv
\]
\[
= -11u + 7v + 7uv
\]

- Answer: \(\boxed{-11u + 7v + 7uv}\)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ -6x^3y^3 + x^2y^2 \\
2. & \ 7y + 7x^2y^3 + 6x^2 \\
3. & \ -11x^2y - 8x^3 \\
4. & \ 2x^2y^2 - 2x^3y \\
5. & \ 5b^2 + 8b + 6 \\
6. & \ -6mn^3 + 2m^3 + 2m^2n^2 \\
7. & \ 8x^3y^3 - 7xy^2 - 1 \\
8. & \ -9x^2 \\
9. & \ -m^2 + 2m^3n^3 \\
10. & \ -3uv - 3u^2v^2 \\
11. & \ 4x - 14y \\
12. & \ 10v^3 \\
13. & \ -6x^2y + 8x^3y \\
14. & \ -a^2b - 6a \\
15. & \ -9xy \\
16. & \ 14m^3n - 9mn^2 \\
17. & \ 3x - 4y^2 \\
18. & \ 14m^3n^2 - 2n^2 \\
19. & \ -11u^3v^2 - u^3v \\
20. & \ -7uv^2 \\
21. & \ -9xy^3 + 9x^2y^2 \\
22. & \ -xy^3 - 2x^3 \\
23. & \ -2b^3 + 3a^2b^3 \\
24. & \ 8x^3y^3 - 2y^2 \\
25. & \ 7m^3 - 9m^3n^3 \\
26. & \ 2x - 6x^3y^2 \\
27. & \ -11u + 7v + 7uv \\
\end{aligned}
}
\]