2.5: Binomial expansion with parameter pp

0606/21/O/N/19 — Question 10 · 8 marks · Binomial

(i)
Expand (3+x)4(3 + x)^{4} evaluating each coefficient.
[3]
(ii)
In the expansion of (x−px)(3+x)4\left(x - \tfrac{p}{x}\right)(3 + x)^{4} the coefficient of xx is zero. Find the value of the constant pp.
[2]
(iii)
Hence find the term independent of xx.
[1]
(iv)
Show that the coefficient of x2x^{2} is 90.
[2]