Name: April
Who is asking: Student
Level of the question: Secondary

Question: What are the 3rd and 4th terms of this sequence: (2x-y)7?
I'm having an issue with there any easier way to get it without completely factoring the whoooole thing out?

Hi April,

There certainly is a better way then expanding the entire expression, it is to use the binomial theorem. You need to use the binomial coefficients which you may have seen before. For integers n and k, with k ≤ n, the binomial coefficients are given by.

I wrote the notation nCk since some high school texts use this notation but I am going to use since this is the notation mathematicians use. Using this notation the binomial theorem states.

For your example you have n = 7, a = 2x and b = -y.

Hence, for example the fifth term is