Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2015  MayJun  (P19709/12)  Q#3
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Question
i. Find the coefficients of in the expansion of .
ii. Find the coefficient of in the expansion of .
Solution
i.
Expression for the general term in the Binomial expansion of is:
First we rewrite the expression in the standard form;
In the given case:
Hence;
Since we are looking for the terms with : we can equate




Now we can find the two terms with ;
Substituting ; 
Substituting ; 














Hence the coefficients of in the expansion of are & respectively.
ii.
It is evident that to get the terms containing in the product of we need;
This will result;
Hence we need first to find the terms with and i.e. in the expansion of .
From (i) we have, in the expansion of ;


Since we are looking for the coefficient of .
Hence the coefficient of is .
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