Question

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

Answer 1

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`).