# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | May-Jun | (P1-9709/11) | Q#1

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**Question**

The term independent of x in the expansion of , where k is a constant, is 540.

**(i) **Find the value of k.

**(ii) **For this value of k, find the coefficient of x^{2} in the expansion.

**Solution**

**(i)
**

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

In the given case:

Hence;

Since we are given the coefficient of the term independent of i.e. , as 540, so we can equate;

However, we need to find for the term independent of i.e. .

Hence, substituting ;

Becomes;

**(ii)
**

We are given that , therefore;

We are required to find the coefficient of x^{2} in the expansion.

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

In the given case:

Hence;

Since we are looking for the coefficient of term with : we can equate;

Therefore;

Hence, coefficient of the term containing is 540.

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