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Find the coefficient of \(x^{4}\) in the binomial expansion of \((1 - 2x)^{6}\).

Further Mathematics
WAEC 2006

Find the coefficient of \(x^{4}\) in the binomial expansion of \((1 - 2x)^{6}\).

  • A. 320
  • B. 240
  • C. -320
  • D. -240
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Correct Answer: Option B
Explanation

\((1 - 2x)^{6} = ^{6}C_{0}(1^{6}) + ^{6}C_{1}(1^{5})(-2x^{1})  + ^{6}C_{2}(1^{4})(-2x^{2}) + ^{6}C_{3}(1^{3})(-2x^{3}) + ^{6}C_{4}(1^{2})(-2x^{4}) + ...\)

\(\text{The coefficient of} x^{4} = 15 \times 16 = 240\)


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