3.76: Binomial expansions and a term independent of $x$

0606/21/M/J/22 — Question 5 · 7 marks · Binomial

(a)(i)

Write down, in ascending powers of

x

, the first three terms in the expansion of

(1 + 4x)^{n}

. Simplify each term.

[2]

(a)(ii)

In the expansion of

(1 + 4x)^{n}(1 - 4x)

, the coefficient of

x^{2}

is 6032. Given that

n > 0

, find the value of

n

[3]

(b)

Find the term independent of

x

in the expansion of

\left(\dfrac{x}{2} - \dfrac{8}{x^{4}}\right)^{10}

[2]

3.76: Binomial expansions and a term independent of xxx