3.66: Binomial expansion in descending powers

0606/13/M/J/23 — Question 5 · 6 marks

(a)
Find the first three terms in the expansion of (4x212x)10\left(4x^{2} - \dfrac{1}{2x}\right)^{10} in descending powers of xx. Give each term in its simplest form.
[3]
(b)
Hence find the coefficient of x16x^{16} in the expansion of (4x212x)10(2x2+1x2)2\left(4x^{2} - \dfrac{1}{2x}\right)^{10}\left(2x^{2} + \dfrac{1}{x^{2}}\right)^{2}.
[3]