# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/13) | Q#8

**Question**

** i. **Find the coefficient of in the expansion of .

** ii. **Find the coefficient of in the expansion of .

** iii. **Hence find the coefficient of in the expansion of .

**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 of : we can equate

Subsequently substituting in:

Since we are interested in the coefficient of ;

ii.

Expression for the general term in the Binomial expansion of is:

In the given case:

Hence;

Since we are looking for the term of : we can equate

Subsequently substituting in:

Since we are interested in the coefficient of ;

iii.

Expression for the Binomial expansion of is:

In the given case:

Hence;

Since terms with appear in and we only consider those terms

From (i) & (ii) terms with ;

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