Simplify algebraic expressions by combining like terms on this educational worksheet.

Let's solve each expression by combining like terms. Like terms are terms that have the same variable raised to the same power (e.g., $3x$ and $5x$ are like terms, but $3x$ and $2y$ are not).

We'll go through each one step by step.

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1. $3x + 5x + 2y$

- Combine $3x + 5x = 8x$
- $2y$ has no like term
- Answer: $8x + 2y$

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

- Combine $2a + 3a = 5a$
- Combine $-4b + b = -3b$
- Answer: $5a - 3b$

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

- Combine $6m - 3m = 3m$
- Combine $2n + 5n = 7n$
- Answer: $3m + 7n$

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4. $4p - 7q - 2p + 9q$

- Combine $4p - 2p = 2p$
- Combine $-7q + 9q = 2q$
- Answer: $2p + 2q$

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5. $8x + 3y - 2x - 6y$

- Combine $8x - 2x = 6x$
- Combine $3y - 6y = -3y$
- Answer: $6x - 3y$

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6. $5a + 2b - 3a + 4b$

- Combine $5a - 3a = 2a$
- Combine $2b + 4b = 6b$
- Answer: $2a + 6b$

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7. $2m - 9n + 7m + 5n$

- Combine $2m + 7m = 9m$
- Combine $-9n + 5n = -4n$
- Answer: $9m - 4n$

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8. $6x + 3y - 4x - 2y$

- Combine $6x - 4x = 2x$
- Combine $3y - 2y = y$
- Answer: $2x + y$

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9. $4a - 5b + 2c - 3a + 4b - c$

- Combine $4a - 3a = a$
- Combine $-5b + 4b = -b$
- Combine $2c - c = c$
- Answer: $a - b + c$

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✔ Final Answers:

| Expression | Simplified |
|----------|------------|
| $3x + 5x + 2y$ | $8x + 2y$ |
| $2a - 4b + 3a + b$ | $5a - 3b$ |
| $6m + 2n - 3m + 5n$ | $3m + 7n$ |
| $4p - 7q - 2p + 9q$ | $2p + 2q$ |
| $8x + 3y - 2x - 6y$ | $6x - 3y$ |
| $5a + 2b - 3a + 4b$ | $2a + 6b$ |
| $2m - 9n + 7m + 5n$ | $9m - 4n$ |
| $6x + 3y - 4x - 2y$ | $2x + y$ |
| $4a - 5b + 2c - 3a + 4b - c$ | $a - b + c$ |

You can now fill these into the boxes on the right! 😊