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