# Thread: Find the coefficient of (x^7)(y^9) in the expansion of ((x-2y)^16)

1. ## Find the coefficient of (x^7)(y^9) in the expansion of ((x-2y)^16)

Hello, I'm having trouble with this question, any help would be greatly appreciated.

Find the coefficient of (x^7)(y^9) in the expansion of ((x-2y)^16). Write your answers as a positive or negative product of prime powers.

Thanks.

2. ## Re: Find the coefficient of (x^7)(y^9) in the expansion of ((x-2y)^16)

Use the Binomial Theorem:

$(a+b)^n = \sum_{k=0}^n \binom{n}{k}a^kb^{n-k}$

Just let $a = x$, $b = -2y$, and $n=16$.