What is the constant term in the expansion of #(x^2-x-2)^15#?

1 Answer
Mar 7, 2017

Answer:

Constant term is #-32768#

Explanation:

In #(x^2-x-2)^15#, we multiply #(x^2-x-2)# with itself #15# times.

When multiply #(x^2-x-2)# with #(x^2-x-2)# for the first time, each term gets multiplied with each term but constant term in their product will be there only when #-2# is multiplied by #-2# and we get the constant term #4# in the product.

So in #(x^2-x-2)^15#, we get constant term when #(-2)# is multiplied with itself #15# times i.e.

constant term is #(-2)^15=-32768# (minus because it is an odd power of #-2#).