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TMUA 2019 · Paper 2 · Question 1 of 20

TMUA 2019 Paper 2 Question 1

Sequences and series — Binomial expansion · picking one term. Try it first; the answer and a full worked solution are below.

TMUA 2019 · Paper 2Sequences and seriesBinomial expansion · picking one term5 options
Find the coefficient of the x4 term in the expansion of x2(2x + 1x)6
  1. A15
  2. B30
  3. C60
  4. D120
  5. E240
Show the answer and worked solution
answer · E
  1. A15
  2. B30
  3. C60
  4. D120
  5. E240
The factor x2 outside means you want the x2 term inside the bracket. A general term of (2x + 1x)6 is (6k)(2x)6−k(1x)k = (6k)26−kx6−2k, so 6 − 2k = 2 gives k = 2. That term is (62)24 = 15 × 16 = 240.