To solve these problems, we need to simplify each expression by combining like terms. Like terms are terms that have the same variable raised to the same power. We add or subtract their coefficients (the numbers in front of the variables).
Let’s go through each one step by step:
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1. 4a + 3b - 2a + 5b
- Combine “a” terms: 4a - 2a = 2a
- Combine “b” terms: 3b + 5b = 8b
→ Final:
2a + 8b
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2. 4y - 2y + 3y - 6
- Combine “y” terms: 4y - 2y + 3y = 5y
- The constant is just -6
→ Final:
5y - 6
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3. 3p - 2q + 3p - 4q
- Combine “p” terms: 3p + 3p = 6p
- Combine “q” terms: -2q - 4q = -6q
→ Final:
6p - 6q
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4. 7c - 3d + 2c - 5d
- Combine “c” terms: 7c + 2c = 9c
- Combine “d” terms: -3d - 5d = -8d
→ Final:
9c - 8d
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5. 6m + 4n - 2m - 3n
- Combine “m” terms: 6m - 2m = 4m
- Combine “n” terms: 4n - 3n = 1n → which is just n
→ Final:
4m + n
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6. 2a + 3b - 2a - 4b
- Combine “a” terms: 2a - 2a = 0a → they cancel out
- Combine “b” terms: 3b - 4b = -1b → which is -b
→ Final:
-b
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7. 4p - 3q + 2p + 5q - 3p
- Combine “p” terms: 4p + 2p - 3p = 3p
- Combine “q” terms: -3q + 5q = 2q
→ Final:
3p + 2q
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8. 9x - 2y + 3x - 2y + 5x - 3x
- Combine “x” terms: 9x + 3x + 5x - 3x = 14x
- Combine “y” terms: -2y - 2y = -4y
→ Final:
14x - 4y
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9. 3x + 2y - z + 2x - y + 4z
- Combine “x” terms: 3x + 2x = 5x
- Combine “y” terms: 2y - y = 1y → just y
- Combine “z” terms: -z + 4z = 3z
→ Final:
5x + y + 3z
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10. 2a - b + 3c - 4a + 2b - 2c
- Combine “a” terms: 2a - 4a = -2a
- Combine “b” terms: -b + 2b = 1b → just b
- Combine “c” terms: 3c - 2c = 1c → just c
→ Final:
-2a + b + c
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Final Answer:
1. 2a + 8b
2. 5y - 6
3. 6p - 6q
4. 9c - 8d
5. 4m + n
6. -b
7. 3p + 2q
8. 14x - 4y
9. 5x + y + 3z
10. -2a + b + c
Parent Tip: Review the logic above to help your child master the concept of combining like terms printable worksheet.
