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

Further Mathematics
WAEC 2025

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

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

We use the binomial theorem:

\((1 - 2x)^6 = \sum_{k=0}^{6} \binom{6}{k}(1)^{6-k}(-2x)^k\)

The \(x^4\) term occurs when \(k = 4\).

So the coefficient of \(x^4\) is: \(\binom{6}{4}(-2)^4\)

Now calculate: \(\binom{6}{4} = 15\)
\((-2)^4 = 16\)

\(\text{Coefficient of } x^4\) = 15 x 16 = 240


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