# 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 ;   