1.1: Binomial expansion and coefficient of x4x^4

0606/11/M/J/18 — Question 9 · 6 marks · Binomial

(i)
Find the first 3 terms in the expansion of (2x116x)8\left(2x - \tfrac{1}{16x}\right)^{8} in descending powers of xx.
[3]
(ii)
Hence find the coefficient of x4x^{4} in the expansion of (2x116x)8(1x2+1)2\left(2x - \tfrac{1}{16x}\right)^{8}\left(\tfrac{1}{x^{2}} + 1\right)^{2}.
[3]