Kenneth ChengMathematical modeling
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Find the coefficient of x⁴y⁵ in the product.

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TOPIC 01

2025 JM01

The x⁻² factor changes the required binomial power.

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Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

Find the coefficient of x⁴y⁵ in the product.

(x+y3x2)(x+y)8\left(x+\frac{y^3}{x^2}\right)(x+y)^8

Official paper · jm01-2025 · I.9 · PDF 3

Official original and suggested answers ↗ · Suggested answer PDF page 5

Skills and prerequisite lessons
  1. Option A6565
  2. Option B8484
  3. Option C9494
  4. Option D127127
  5. Option E176176

Working and explanation

BUILD THE REASONING

Hint 1
There are two ways to obtain the requested powers.
Hint 2
Track exponents after multiplying by x or y³/x².
Worked solution

  1. The x term needs x³y⁵ from the binomial.

    (85)=56\binom85=56

  2. The other term needs x⁶y²; add the contributions.

    (82)=28,56+28=84\binom82=28,\quad56+28=84

B: 84.

Checks and common pitfalls: The x⁻² factor changes the required binomial power.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • The x term needs x³y⁵ from the binomial.
    (85)=56\binom85=56
  • The other term needs x⁶y²; add the contributions.
    (82)=28,56+28=84\binom82=28,\quad56+28=84

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Curriculum and source notes ↗