# Binomial Theorem

• August 9th 2006, 04:56 AM
kodirl
Discrete maths
Q.use the binomial theorem to find the coefficient of x^5y^3 in (x-2y)^8.
• August 9th 2006, 05:31 AM
CaptainBlack
Quote:

Originally Posted by kodirl
Q.use the binomial theorem to find the coefficient of x^5y^3 in (x-2y)^8.

The binomial theorem tell you that:

$
(x-2y)^8=\sum_{r=0}^8 {8 \choose r}x^{n-r}(-2y)^{r}
$

So the coefficient of $x^5y^3$ is:

$
{8 \choose 3}(-2)^3=-\frac{8!\times 8}{5!\ 3!}
$

RonL