Question

     i.       Find the first three terms, in ascending powers of , in the expansion of 

a.  

b.  

   ii.       Hence find the coefficient of  in the expansion of .

Solution

i.
 

a)
 

Expression for the Binomial expansion of  is:

First we rewrite the given equation in the standard form;

In the given case:

Hence;

b)
 

Expression for the Binomial expansion of  is:

In the given case:

Hence;

ii.
 

To find the coefficient of  in the expansion of .

From (i) we have;

Therefore;

Since we are interested only in terms with

Hence coefficient of  is 3.