Binomial Theorem

**kodirl** · August 9th 2006, 03:56 AM

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

**CaptainBlack** · August 9th 2006, 04:31 AM

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:

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

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

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

RonL

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