Binomial Expansion (Edexcel International AS Maths: Pure 2)

Expand 

Find the coefficient of the term in  in the expansion of .

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

Use your answer to part (a) to estimate .

In the expansion of , the coefficient of the  term is 96.
Given that , find the value of .

Find the first three terms in the expansion of .

Use your answer to part (a) to estimate .

In the expansion of , the coefficient of the  term is equal to the coefficient of the  term.  Find the value of .

In the expansion of , the coefficient of the  term is four times the coefficient of the  term.  Find the possible values of .

Find the first three terms in the expansion of .

Given that  is small such that and higher powers of can be ignored show that

In the expansion of , the coefficients of the  term and the  term are equal.

Find  in terms of .

In the expansion of , the coefficient of the  term is equal to the coefficient of the  term.

Show that .

Given that and  are integers, and that , find the values of  and .

Fully expand .

Fully expand  .

Find the coefficient of the term in in the expansion of 

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

Use your answer to part (a) to estimate .

In the expansion of , the coefficient of the  term is 19 440.
Given that  is a positive integer find the value of .

In the expansion of  the coefficient of the  term is equal to the coefficient of the  term.  Find the value of .

Find the first three terms in the expansion of .

Given that  is small such that  and higher powers of  can be ignored show that

In the expansion of , the coefficients of the  term and the  term are equal.

Find  in terms of .

In the expansion of  the coefficient of the  term is 84.

Find the value of .

In the expansion of  the coefficient of the  term is 216.

In the expansion of  the coefficient of the  term is 4860.

Find the possible values of  and .

Expand .

Find the coefficient of the term in  in the expansion of .

Given that  find the value of .

Use the first three terms, in ascending powers of , in the expansion of  to find an approximation for .

Using your calculator, find the percentage error in the approximation from part (a) to the exact value of .

In the expansion of , the coefficient of the  term is -10.
Find the possible values of .

In the expansion of  , the coefficient of the  term is equal to the coefficient of the  term.  Find the values of , giving your answers in the form , where  and  are integers to be found.

Find the first three terms in the expansion of .

Given that  is small such that  and higher powers of  can be ignored show that

In the expansion of , the coefficient of the  term is double that of the  term.  Find  in terms of .

In the expansion of  the coefficient of the  term is -3240.

Find the value of .

In the expansion of  the coefficient of the  term is -870 912.

In the expansion of  the coefficient of the  term is -1 557 135 360.

Find the possible values of  and .