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

Mar 7, 2017

Constant term is $- 32768$

#### Explanation:

In ${\left({x}^{2} - x - 2\right)}^{15}$, we multiply $\left({x}^{2} - x - 2\right)$ with itself $15$ times.

When multiply $\left({x}^{2} - x - 2\right)$ with $\left({x}^{2} - x - 2\right)$ 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 ${\left({x}^{2} - x - 2\right)}^{15}$, we get constant term when $\left(- 2\right)$ is multiplied with itself $15$ times i.e.

constant term is ${\left(- 2\right)}^{15} = - 32768$ (minus because it is an odd power of $- 2$).