# Math Help - binomial theorem!

1. ## binomial theorem!

use the binomial theorem to determine the coefficient of x^33 in the expansion of(1/4-2x^3)^17

2. I think it is:

$(\frac{1}{4})^{17-11}\cdot (-2)^{11} \cdot \binom{17}{11} = -6188$

Not sure though...

3. Originally Posted by jordan1
use the binomial theorem to determine the coefficient of x^33 in the expansion of(1/4-2x^3)^17
The general term is ${17 \choose r} \left( \frac{1}{4} \right)^r (-2 x^3)^{17-r} = {17 \choose r} \left( \frac{1}{4} \right) (-2)^{17-r} x^{51 - 3r}$.

Now substitute the value of $r$ that satisfies $51 - 3r = 33$ into ${17 \choose r} \left( \frac{1}{4} \right)^r (-2)^{17-r}$.