Write down the first three terms in the expansion, in ascending powers of \(x\), of \((2+ax)^8\), where \(a\) is a constant. Give the terms in their simplest form.
In the expansion of \((1+2x-4x^2)(2+ax)^8\), the coefficient of \(x^2\) is \(22\) times the coefficient of \(x\). Given that \(a\) is positive, calculate the value of \(a\).
Explain why there is no even power of \(x\) in the expansion of \(\left(\dfrac{x^3}{2}+\dfrac2{3x}\right)^{15}\).
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Answer:(a) \(256+1024ax+1792a^2x^2\); (b) \(a=12\); (c) every exponent \(45-4r\) is odd.