Let’s solve each problem step by step. We’re combining like terms — that means we add or subtract terms that have the same variable (like “a” with “a”, “b” with “b”, etc.). Constants (numbers without variables) stay as they are.
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1. 4a + 3b - 2a + 5b
Group like terms:
- a terms: 4a - 2a =
2a
- b terms: 3b + 5b =
8b
→ Final:
2a + 8b
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2. 4y - 2y + 3y - 6
Group like terms:
- y terms: 4y - 2y + 3y = (4 - 2 + 3)y =
5y
- constant:
-6
→ Final:
5y - 6
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3. 3p - 2q + 3p - 4q
Group like terms:
- p terms: 3p + 3p =
6p
- q terms: -2q - 4q =
-6q
→ Final:
6p - 6q
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4. 7c - 3d + 2c - 5d
Group like terms:
- c terms: 7c + 2c =
9c
- d terms: -3d - 5d =
-8d
→ Final:
9c - 8d
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5. 6m + 4n - 2m - 3n
Group like terms:
- m terms: 6m - 2m =
4m
- n terms: 4n - 3n =
1n → just write
n
→ Final:
4m + n
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6. 2a + 3b - 2a - 4b
Group like terms:
- a terms: 2a - 2a =
0a → disappears
- b terms: 3b - 4b =
-1b → just write
-b
→ Final:
-b
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7. 4p - 3q + 2p + 5q - 3p
Group like terms:
- p terms: 4p + 2p - 3p = (4 + 2 - 3)p =
3p
- q terms: -3q + 5q =
2q
→ Final:
3p + 2q
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8. 9x - 2y + 3x - 2y + 5x - 3x
Group like terms:
- x terms: 9x + 3x + 5x - 3x = (9 + 3 + 5 - 3)x =
14x
- y terms: -2y - 2y =
-4y
→ Final:
14x - 4y
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9. 3x + 2y - z + 2x - y + 4z
Group like terms:
- x terms: 3x + 2x =
5x
- y terms: 2y - y =
1y → just
y
- z terms: -z + 4z =
3z
→ Final:
5x + y + 3z
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10. 2a - b + 3c - 4a + 2b - 2c
Group like terms:
- a terms: 2a - 4a =
-2a
- b terms: -b + 2b =
1b → just
b
- 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 combine like terms equations worksheet.
