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 (like x, y, a, b, etc.). We add or subtract their coefficients (the numbers in front).

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1. 3x + 5x + 2y

- Combine x terms: 3x + 5x = 8x
- The 2y has no other y term to combine with → stays as is
→ 8x + 2y

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

- Combine a terms: 2a + 3a = 5a
- Combine b terms: -4b + b = -3b
→ 5a - 3b

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

- Combine m terms: 6m - 3m = 3m
- Combine n terms: 2n + 5n = 7n
→ 3m + 7n

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

- Combine p terms: 4p - 2p = 2p
- Combine q terms: -7q + 9q = 2q
→ 2p + 2q

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

- Combine x terms: 8x - 2x = 6x
- Combine y terms: 3y - 6y = -3y
→ 6x - 3y

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

- Combine a terms: 5a - 3a = 2a
- Combine b terms: 2b + 4b = 6b
→ 2a + 6b

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

- Combine m terms: 2m + 7m = 9m
- Combine n terms: -9n + 5n = -4n
→ 9m - 4n

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

- Combine x terms: 6x - 4x = 2x
- Combine y terms: 3y - 2y = y
→ 2x + y

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

- Combine a terms: 4a - 3a = a
- Combine b terms: -5b + 4b = -b
- Combine c terms: 2c - c = c
→ a - b + c

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Final Answer:
1. 8x + 2y
2. 5a - 3b
3. 3m + 7n
4. 2p + 2q
5. 6x - 3y
6. 2a + 6b
7. 9m - 4n
8. 2x + y
9. a - b + c