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

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Question

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

ii.       It is given that, when is expanded, there is no term in . Find the value of the constant .

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 that coefficient of the term containing in the product of is zero.

We have found in (i) that in the expansion of we have terms;  Therefore can be written for terms containing as follows; It can be expanded as; As per given condition coefficient of the term containing is zero, therefore;  Hence;     