301 Moved Permanently - Free Printable

Problem: Simplify each polynomial expression.

We will solve each problem step by step, combining like terms where necessary.

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

- Distribute the negative sign:
\[
4x^2y^3 - 2x - 2x - 2x^2y^3
\]
- Combine like terms:
\[
(4x^2y^3 - 2x^2y^3) + (-2x - 2x) = 2x^2y^3 - 4x
\]

Answer: C) \( 2x^2y^3 - 4x \)

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#### 2. Simplify \( (mn^2 + 3) - (7 - 5mn^2) \)

- Distribute the negative sign:
\[
mn^2 + 3 - 7 + 5mn^2
\]
- Combine like terms:
\[
(mn^2 + 5mn^2) + (3 - 7) = 6mn^2 - 4
\]

Answer: C) \( 6mn^2 - 4 \)

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#### 3. Simplify \( (-2 - 2u^3) - (-5u^3 + 5) \)

- Distribute the negative sign:
\[
-2 - 2u^3 + 5u^3 - 5
\]
- Combine like terms:
\[
(-2 - 5) + (-2u^3 + 5u^3) = -7 + 3u^3
\]

Answer: B) \( 3u^3 - 7 \)

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

- Combine like terms:
\[
(-6x^3 - 2x^3) + (3x^2y^3 + 7x^2y^3) = -8x^3 + 10x^2y^3
\]

Answer: B) \( 10x^2y^3 - 8x^3 \)

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#### 5. Simplify \( (-3 + 3x) - (-7x + 2) \)

- Distribute the negative sign:
\[
-3 + 3x + 7x - 2
\]
- Combine like terms:
\[
(-3 - 2) + (3x + 7x) = -5 + 10x
\]

Answer: D) \( 10x - 5 \)

---

#### 6. Simplify \( (-2u^2 + uv) + (8u^2 - 5uv) \)

- Combine like terms:
\[
(-2u^2 + 8u^2) + (uv - 5uv) = 6u^2 - 4uv
\]

Answer: C) \( 6u^2 - 4uv \)

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#### 7. Simplify \( (-6a^2b^3 - ab) + (-2ab - 5a^2b^3) \)

- Combine like terms:
\[
(-6a^2b^3 - 5a^2b^3) + (-ab - 2ab) = -11a^2b^3 - 3ab
\]

Answer: A) \( -11a^2b^3 - 3ab \)

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#### 8. Simplify \( (7y + 3xy) + (3y + 5xy) \)

- Combine like terms:
\[
(7y + 3y) + (3xy + 5xy) = 10y + 8xy
\]

Answer: B) \( 8xy + 10y \)

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#### 9. Simplify \( (4x^3y - 1) - (8x^3y - 2) \)

- Distribute the negative sign:
\[
4x^3y - 1 - 8x^3y + 2
\]
- Combine like terms:
\[
(4x^3y - 8x^3y) + (-1 + 2) = -4x^3y + 1
\]

Answer: A) \( -4x^3y + 1 \)

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#### 10. Simplify \( (x^3y^2 + 3x^3y) + (-3x^3y + 8x^3y^2) \)

- Combine like terms:
\[
(x^3y^2 + 8x^3y^2) + (3x^3y - 3x^3y) = 9x^3y^2 + 0x^3y = 9x^3y^2
\]

Answer: D) \( 9x^3y^2 \)

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#### 11. Simplify \( (-3xy - x^2y) - (2x^2y + xy) \)

- Distribute the negative sign:
\[
-3xy - x^2y - 2x^2y - xy
\]
- Combine like terms:
\[
(-3xy - xy) + (-x^2y - 2x^2y) = -4xy - 3x^2y
\]

Answer: C) \( -3x^2y - 4xy \)

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#### 12. Simplify \( (-6uv + 4v^3) + (7uv - 6v^3) \)

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

Answer: C) \( -2v^3 - uv \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. \text{C} & 2. \text{C} & 3. \text{B} & 4. \text{B} \\
5. \text{D} & 6. \text{C} & 7. \text{A} & 8. \text{B} \\
9. \text{A} & 10. \text{D} & 11. \text{C} & 12. \text{C}
\end{array}
}
\]