9709 P3 - Jun 2009 - Q5
2034
When \((1 + 2x)(1 + ax)^{\frac{2}{3}}\), where \(a\) is a constant, is expanded in ascending powers of \(x\), the coefficient of the term in \(x\) is zero.
(i) Find the value of \(a\).
(ii) When \(a\) has this value, find the term in \(x^3\) in the expansion of \((1 + 2x)(1 + ax)^{\frac{2}{3}}\), simplifying the coefficient.
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