1.21: Binomial coefficient and independent term

0606/13/O/N/18 — Question 1 · 6 marks · Binomial

(a)
In the expansion of (2+px)5(2 + px)^{5} the coefficient of x3x^{3} is equal to −825-\tfrac{8}{25}. Find the value of the constant pp.
[3]
(b)
Find the term independent of xx in the expansion of (2x2+14x2)8\left(2x^{2} + \tfrac{1}{4x^{2}}\right)^{8}.
[3]