# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/12) | Q#4

Question

Find the term independent of in the expansion of

i. ii. Solution

i.

Expression for the general term in the Binomial expansion of is: In the given case : Hence;      Since we are looking for the coefficient of the term independent of i.e. , so we can  equate       Hence, substituting ; Becomes;      Hence coefficient of the term independent of i.e. is .

ii.

It is evident that to get the terms independent of in the product of , we need the terms in the expansion of which are independent of and contain . We have found in (i) that term in the expansion of which is independent of is .

Hence, we need a term in the expansion of with .

Expression for the general term in the Binomial expansion of is: In the given case : Hence;      Since we are looking for the coefficient of the term independent of i.e. , so we can  equate       Hence, substituting ; Becomes;      Hence coefficient of the term containing i.e. is .

Therefore,   Retaining terms independent of ;  