The coefficient of \(x^2\) in the power series expansion of \[ \frac{2x}{(x-1)(x+2)^2} \] when \(|x|<1\) is
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For \( (1+kx)^{-n} \), the coefficient of \( x^r \) is \( (-1)^r \binom{n+r-1}{r} k^r \). Using this general formula helps avoid manual expansion errors.