# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/11) | Q#3

Question

i.       Find the first three terms, in ascending powers of , in the expansion of

a.

b.

ii.       Hence find the coefficient of  in the expansion of .

Solution

i.

a)

Expression for the Binomial expansion of  is:

First we rewrite the given equation in the standard form;

In the given case:

Hence;

b)

Expression for the Binomial expansion of  is:

In the given case:

Hence;

ii.

To find the coefficient of  in the expansion of .

From (i) we have;

Therefore;

Since we are interested only in terms with

Hence coefficient of  is 3.