# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2004 | May-Jun | (P1-9709/01) | Q#4

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Question

Find the coefficient 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 term with , we can  equate

Finally substituting  in:

Therefore the coefficient of  is .

ii.

To find the coefficient of  in the expansion of

First of all we must notice that there will be two terms with . One is product of 1 from  and
from the expansion of . Second will be product of  from  and  from the expansion of .

Therefore we look for the terms containing  &  in the expansion of

We know that expression for the general term in the Binomial expansion of  is:

In the given case:

Hence;

Since we are looking for the term with , we can  equate

Finally substituting  in:

Therefore the term with  is .

From (i) the term with  is :

Therefore  can be expanded in a limited way as:

Therefore, the coefficient of is .