Using the binomial theorem explicitly, give the 15th term in the expansion of (-2x + 1)^19

Let's rewrite the binomial as:




Using the binomial expansion, we get:


For the 15th term, we want the term where r is equal to 14, because of the fact that the first term starts when r = 0. Thus, for the 15th term, we need to include the 0th or the first term of the binomial expansion.

Thus, the fifteenth term is: