Let’s solve each problem one by one. We’ll combine like terms and simplify carefully.
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Problem 1: (5a + 4) - (5a + 3)
Subtract the second group from the first. Be careful with the minus sign — it changes the signs inside the parentheses.
= 5a + 4 - 5a - 3
Now combine like terms:
5a - 5a = 0
4 - 3 = 1
→ Answer:
1
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Problem 2: (2y² + 1) + (y² - 2y + 1)
Add the two groups together. Combine like terms.
= 2y² + y² - 2y + 1 + 1
= (2+1)y² - 2y + (1+1)
= 3y² - 2y + 2
→ Answer:
3y² - 2y + 2
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Problem 3: (7 + 2m²) + (2m² - 2)
Add them up. Rearrange to group like terms.
= 2m² + 2m² + 7 - 2
= 4m² + 5
→ Answer:
4m² + 5
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Problem 4: 4(x + 5) - 5(x² + 4x + 7)
First, distribute the 4 and the -5 into their parentheses.
= 4x + 20 - 5x² - 20x - 35
Now combine like terms:
-5x² (only x² term)
4x - 20x = -16x
20 - 35 = -15
→ Answer:
-5x² - 16x - 15
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Problem 5: 5(d + 3) - 9(d² - 3d + 2)
Distribute 5 and -9.
= 5d + 15 - 9d² + 27d - 18
Combine like terms:
-9d² (only d² term)
5d + 27d = 32d
15 - 18 = -3
→ Answer:
-9d² + 32d - 3
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Problem 6: (4r³ + 3r⁴) - (r⁴ - 5r³)
Distribute the minus sign across the second group.
= 4r³ + 3r⁴ - r⁴ + 5r³
Combine like terms:
3r⁴ - r⁴ = 2r⁴
4r³ + 5r³ = 9r³
→ Answer:
2r⁴ + 9r³
*(Note: Usually we write polynomials in descending order of exponents, so this is correct as written.)*
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Problem 7: (3x² - 6x⁵ - 2x) - (-2x² - 6x⁵ + 2x)
Distribute the minus sign: change all signs in the second group.
= 3x² - 6x⁵ - 2x + 2x² + 6x⁵ - 2x
Now combine like terms:
-6x⁵ + 6x⁵ = 0 → cancels out
3x² + 2x² = 5x²
-2x - 2x = -4x
→ Answer:
5x² - 4x
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Problem 8: (-12y⁴ + 10y⁵ + 2y³) + (14y³ + 23y⁵ + 8y⁴)
Add them together. Group like terms.
Start with highest power:
y⁵ terms: 10y⁵ + 23y⁵ = 33y⁵
y⁴ terms: -12y⁴ + 8y⁴ = -4y⁴
y³ terms: 2y³ + 14y³ = 16y³
→ Answer:
33y⁵ - 4y⁴ + 16y³
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Final Answers:
1. 1
2. 3y² - 2y + 2
3. 4m² + 5
4. -5x² - 16x - 15
5. -9d² + 32d - 3
6. 2r⁴ + 9r³
7. 5x² - 4x
8. 33y⁵ - 4y⁴ + 16y³
Parent Tip: Review the logic above to help your child master the concept of algebra 1 adding and subtracting polynomials worksheet.
