# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/13) | Q#8

Question

i.       Find the coefficient of  in the expansion of .

ii.       Find the coefficient of  in the expansion of .

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

Solution

i.

Expression for the general term in the Binomial expansion of  is:

In the given case:

Hence;

Since we are looking for the term of   : we can  equate

Subsequently substituting  in:

Since we are interested in the coefficient of ;

ii.

Expression for the general term in the Binomial expansion of  is:

In the given case:

Hence;

Since we are looking for the term of   : we can equate

Subsequently substituting  in:

Since we are interested in the coefficient of ;

iii.

Expression for the Binomial expansion of  is:

In the given case:

Hence;

Since terms with  appear in  and  we only consider those terms

From (i) & (ii) terms with ;