By considering the general term in the binomial expansion of \(\left(2x-\dfrac1{x^2}\right)^8\), explain why no term is independent of \(x\) in this expansion.[3]
Find the first 3 terms in the expansion of \(\left(2x-\dfrac1{x^2}\right)^8\) in descending powers of \(x\). Give the terms in their simplest form.[2]
Find the coefficient of \(x^2\) in the expansion of \(\left(\dfrac1{x^3}+5\right)\left(2x-\dfrac1{x^2}\right)^8\).[2]
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Answer:(a) Constant term would require the inadmissible index \(r=\dfrac83\). (b) \(256x^8-1024x^5+1792x^2\). (c) \(7936\).