3.22: Binomial coefficient and term independent of yy

0606/11/O/N/24 — Question 5 · 4 marks

(a)
In the expansion of (1+kx)15(1 + kx)^{15}, where kk is a constant, the coefficient of x3x^{3} is 29120-29120. Find the value of kk.
[2]
(b)
Find the term independent of yy in the expansion of (y82y2)12\left(\dfrac{y}{8} - \dfrac{2}{y^{2}}\right)^{12}.
[2]