Polynomials-Addition-3 Worksheets - Free Printable

Problem: Simplify the given polynomial expressions by adding them together.

The task involves adding pairs of polynomials and simplifying the result. Let's solve each problem step by step.

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#### 1. $(5x^2 + 2x^3) + (2x^2 - 5x)$

- Combine like terms:
- $x^3$ terms: $2x^3$
- $x^2$ terms: $5x^2 + 2x^2 = 7x^2$
- $x$ terms: $-5x$
- Constant terms: None

- Simplified expression:
$$
2x^3 + 7x^2 - 5x
$$

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#### 2. $(1 + 2x^2) + (3 + 3x^2)$

- Combine like terms:
- $x^2$ terms: $2x^2 + 3x^2 = 5x^2$
- Constant terms: $1 + 3 = 4$

- Simplified expression:
$$
5x^2 + 4
$$

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#### 3. $(2x^4 + 4x^2) + (2x^2 - x)$

- Combine like terms:
- $x^4$ terms: $2x^4$
- $x^2$ terms: $4x^2 + 2x^2 = 6x^2$
- $x$ terms: $-x$
- Constant terms: None

- Simplified expression:
$$
2x^4 + 6x^2 - x
$$

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#### 4. $(5x^4 - x) + (3x - 3x^2)$

- Combine like terms:
- $x^4$ terms: $5x^4$
- $x^2$ terms: $-3x^2$
- $x$ terms: $-x + 3x = 2x$
- Constant terms: None

- Simplified expression:
$$
5x^4 - 3x^2 + 2x
$$

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#### 5. $(2 + 3x^2) + (3 + 3x^2)$

- Combine like terms:
- $x^2$ terms: $3x^2 + 3x^2 = 6x^2$
- Constant terms: $2 + 3 = 5$

- Simplified expression:
$$
6x^2 + 5
$$

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#### 6. $(x^2 + 3) + (2x^2 - 5)$

- Combine like terms:
- $x^2$ terms: $x^2 + 2x^2 = 3x^2$
- Constant terms: $3 - 5 = -2$

- Simplified expression:
$$
3x^2 - 2
$$

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#### 7. $(5x^2 + x^3) + (x^4 - 4x^2)$

- Combine like terms:
- $x^4$ terms: $x^4$
- $x^3$ terms: $x^3$
- $x^2$ terms: $5x^2 - 4x^2 = x^2$
- Constant terms: None

- Simplified expression:
$$
x^4 + x^3 + x^2
$$

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#### 8. $(3n - 2n^2) + (4n^2 + n)$

- Combine like terms:
- $n^2$ terms: $-2n^2 + 4n^2 = 2n^2$
- $n$ terms: $3n + n = 4n$
- Constant terms: None

- Simplified expression:
$$
2n^2 + 4n
$$

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#### 9. $(4n^2 + 4) + (5 - n^2)$

- Combine like terms:
- $n^2$ terms: $4n^2 - n^2 = 3n^2$
- Constant terms: $4 + 5 = 9$

- Simplified expression:
$$
3n^2 + 9
$$

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#### 10. $(2x^2 - 5x^2) + (5x^2 - 3x^2)$

- Combine like terms:
- $x^2$ terms: $2x^2 - 5x^2 + 5x^2 - 3x^2 = -x^2$

- Simplified expression:
$$
-x^2
$$

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Final Answers:

$$
\boxed{
\begin{aligned}
1. & \quad 2x^3 + 7x^2 - 5x \\
2. & \quad 5x^2 + 4 \\
3. & \quad 2x^4 + 6x^2 - x \\
4. & \quad 5x^4 - 3x^2 + 2x \\
5. & \quad 6x^2 + 5 \\
6. & \quad 3x^2 - 2 \\
7. & \quad x^4 + x^3 + x^2 \\
8. & \quad 2n^2 + 4n \\
9. & \quad 3n^2 + 9 \\
10. & \quad -x^2
\end{aligned}
}
$$