# 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 x2 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 x2 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.