Let’s go through each problem one by one. We’re simplifying expressions by combining like terms — that means we add or subtract the coefficients of terms that have the same variable and exponent.
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Problem 1:
(-7g² + 6g - 8) - (5g² - 2g + 4)
First, distribute the minus sign to the second group:
= -7g² + 6g - 8 - 5g² + 2g - 4
Now combine like terms:
- g² terms: -7g² - 5g² = -12g²
- g terms: 6g + 2g = 8g
- constants: -8 - 4 = -12
✔ Final:
-12g² + 8g - 12
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Problem 2:
(7b² + 3b + 7) + (3b² - 6b - 8)
Just add like terms:
- b²: 7b² + 3b² = 10b²
- b: 3b - 6b = -3b
- constants: 7 - 8 = -1
✔ Final:
10b² - 3b - 1
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Problem 3:
(6k² - 3k + 8) - (-k² - 2k - 9)
Distribute the minus sign:
= 6k² - 3k + 8 + k² + 2k + 9
Combine:
- k²: 6k² + k² = 7k²
- k: -3k + 2k = -k
- constants: 8 + 9 = 17
✔ Final:
7k² - k + 17
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Problem 4:
(6v² - v - 1) + (-4v² - 9v + 9)
Add like terms:
- v²: 6v² - 4v² = 2v²
- v: -v - 9v = -10v
- constants: -1 + 9 = 8
✔ Final:
2v² - 10v + 8
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Problem 5:
(4p² + 2p + 9) + (-5p² - 5p - 2)
Add:
- p²: 4p² - 5p² = -p²
- p: 2p - 5p = -3p
- constants: 9 - 2 = 7
✔ Final:
-p² - 3p + 7
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Problem 6:
(-9f² - f - 7) + (6f² + f - 5)
Add:
- f²: -9f² + 6f² = -3f²
- f: -f + f = 0 → cancel out
- constants: -7 - 5 = -12
✔ Final:
-3f² - 12
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Problem 7:
(8q² - 7q - 1) + (-6q² + 8q + 7)
Add:
- q²: 8q² - 6q² = 2q²
- q: -7q + 8q = q
- constants: -1 + 7 = 6
✔ Final:
2q² + q + 6
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Problem 8:
(-8c² - 9c + 9) + (-5c² - 8c - 6)
Add:
- c²: -8c² - 5c² = -13c²
- c: -9c - 8c = -17c
- constants: 9 - 6 = 3
✔ Final:
-13c² - 17c + 3
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Problem 9:
(9r² - 5r - 7) + (8r² + 8r + 6)
Add:
- r²: 9r² + 8r² = 17r²
- r: -5r + 8r = 3r
- constants: -7 + 6 = -1
✔ Final:
17r² + 3r - 1
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Problem 10:
(4k² - 9k - 8) + (-3k² + 8k + 2)
Add:
- k²: 4k² - 3k² = k²
- k: -9k + 8k = -k
- constants: -8 + 2 = -6
✔ Final:
k² - k - 6
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Final Answer:
1. -12g² + 8g - 12
2. 10b² - 3b - 1
3. 7k² - k + 17
4. 2v² - 10v + 8
5. -p² - 3p + 7
6. -3f² - 12
7. 2q² + q + 6
8. -13c² - 17c + 3
9. 17r² + 3r - 1
10. k² - k - 6
Parent Tip: Review the logic above to help your child master the concept of algebra worksheet answers.
