Let's solve each of the algebraic expressions step by step and explain the solutions.
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Problem 9:
(x² – 5x + 2) – (3x² + x – 1)
Step-by-step:
Distribute the negative sign to each term in the second parentheses:
= x² – 5x + 2 – 3x² – x + 1
Now combine like terms:
- x² – 3x² = –2x²
- –5x – x = –6x
- 2 + 1 = 3
Answer:
–2x² – 6x + 3
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Problem 10:
(3a + 4b) + (6a – 6b)
Combine like terms:
- 3a + 6a = 9a
- 4b – 6b = –2b
Answer:
9a – 2b
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Problem 11:
2a(4b + 5)
Use the distributive property:
= 2a × 4b + 2a × 5
= 8ab + 10a
Answer:
8ab + 10a
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Problem 12:
3x²(2xy – 3xy² + 4x²y³)
Distribute 3x² to each term inside the parentheses:
- 3x² × 2xy = 6x³y
- 3x² × (–3xy²) = –9x³y²
- 3x² × 4x²y³ = 12x⁴y³
Answer:
6x³y – 9x³y² + 12x⁴y³
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Problem 13:
(n – 9)(n + 7)
Use the FOIL method (First, Outer, Inner, Last):
- First: n × n = n²
- Outer: n × 7 = 7n
- Inner: –9 × n = –9n
- Last: –9 × 7 = –63
Now combine:
n² + 7n – 9n – 63 = n² – 2n – 63
Answer:
n² – 2n – 63
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Problem 14:
(a + 4)(a – 6)
Again, use FOIL:
- First: a × a = a²
- Outer: a × (–6) = –6a
- Inner: 4 × a = 4a
- Last: 4 × (–6) = –24
Combine:
a² – 6a + 4a – 24 = a² – 2a – 24
Answer:
a² – 2a – 24
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✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 9 | –2x² – 6x + 3 |
| 10 | 9a – 2b |
| 11 | 8ab + 10a |
| 12 | 6x³y – 9x³y² + 12x⁴y³ |
| 13 | n² – 2n – 63 |
| 14 | a² – 2a – 24 |
Let me know if you'd like these explained with diagrams or visual steps!
Parent Tip: Review the logic above to help your child master the concept of operations on polynomials worksheet.
