## Finding a Coefficient of a Power of x in a Binomial Expansion

In the binomial expansion ofthe coefficient ofisThis is the (r+1) ^{th } term in the binomial expansion ofin ascending powers of

Suppose thatandTo find the coefficient ofin the binomial expansion ofputthen the coefficient ofis and the coefficient ofis

If bothandare terms in x then things get slightly more complicated.

Suppose we want to find the coefficient ofin the binomial expansion of

andso the coefficient ofisand the (r+1) ^{th }term is

Putthenso the coeeficient ofis