Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2018 | Feb-Mar | (P1-9709/12) | Q#2

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Question

     i.       Find the coefficients of  and  in the expansion of .

   ii.       Hence 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.
 

To find the term with   in the expansion of

From (i) we have;

Therefore;

We are interested only in coefficient of which is equal to -140.

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