3.80: Binomial expansion $(2 + ax)^{n}$ with $64 + bx + cx^{2}$

0606/11/O/N/21 — Question 7 · 7 marks · Binomial

The first three terms, in ascending powers of

x

, in the expansion of

(2 + ax)^{n}

can be written as

64 + bx + cx^{2}

, where

n

a

b

and

c

are constants.

(a)

Find the value of

n

[1]

(b)

Show that

5b^{2} = 768c

[4]

(c)

Given that

b = 12

, find the exact value of

a

and of

c

[2]

3.80: Binomial expansion (2+ax)n(2 + ax)^{n}(2+ax)n with 64+bx+cx264 + bx + cx^{2}64+bx+cx2