1.4: Binomial expansion and coefficient of x7x^7

0606/11/O/N/16 — Question 4 · 5 marks · Binomial

(i)
Find the first 3 terms in the expansion of (2x213x)5\left(2x^{2} - \tfrac{1}{3x}\right)^{5}, in descending powers of xx.
[3]
(ii)
Hence find the coefficient of x7x^{7} in the expansion of (3+1x3)(2x213x)5\left(3 + \tfrac{1}{x^{3}}\right)\left(2x^{2} - \tfrac{1}{3x}\right)^{5}.
[2]