# 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

Hits: 230

**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 .

## Comments