2025 Beatty Sec 3 EOY Q10

2025 Beatty Sec 3 EOY Q10

Secondary 3
10 marks
    1. Write down and simplify the first four terms, in descending powers of \(x\), in the expansion of \(\left(x-\dfrac2x\right)^{10}\).[2]
    2. Hence, find the coefficient of \(x^{10}\) in the expansion of \((2+3x)^2\left(x-\dfrac2x\right)^{10}\).[3]
  2. Find the value of \(n\) given that the coefficients of \(x\) and \(x^2\) in the expansion of \((2+3x)^n\) are in the ratio \(4:57\).[5]

Solution:

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Answer:(a)(i) \(x^{10}-20x^8+180x^6-960x^4\); (ii) \(-176\); (b) \(n=20\).

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