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O-Level Binomial expansions: worked solution
2 marks. Full working, one step per line.
Question
Expand (2 − 3/x)⁸ and write, in simplified form, its first three terms in descending powers of x.
Worked answer
General term: C(8,r) (2)^(8-r) (-3/x)^r = C(8,r) 2^(8-r) (-3)^r x^(-r). Descending powers of x means smallest r first (x⁰, x⁻¹, x⁻²): r=0: 2⁸ = 256 r=1: C(8,1)·2⁷·(-3) = 8·128·(-3) = -3072, giving -3072/x r=2: C(8,2)·2⁶·(-3)² = 28·64·9 = 16128, giving 16128/x² First three terms: 256 - 3072/x + 16128/x²
Practise this topic
This question is part of O-Level Binomial expansions, in O-Level Additional Maths (A-Maths).
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