# Thread: Using the Binomial Thm.

1. ## Using the Binomial Thm.

Find the coefficients of x^5y^13 in the expansion of (3x - 2y)^18

Can someone show the steps. Thanks

2. Originally Posted by jzellt
Find the coefficients of x^5y^13 in the expansion of (3x - 2y)^18

Can someone show the steps. Thanks
Can you write down the general term?

3. I started by writing: 18C0 * (3x)^18 * (-2y)^0 + 18C1 * (3x)^17 * (-2y)^ 1 + ...

Am I going about it the wrong way?

4. Originally Posted by jzellt
I started by writing: 18C0 * (3x)^18 * (-2y)^0 + 18C1 * (3x)^17 * (-2y)^ 1 + ...

Am I going about it the wrong way?
Yes you are.

The general term is $\displaystyle {18 \choose r} (3x)^{18 - r} (-2y)^r$.

Simplify this. Isolate the coefficient. Then see if there's a good value of r to use ....

5. Thanks for your time, but I'm still not understanding what to do....

6. Originally Posted by jzellt
Thanks for your time, but I'm still not understanding what to do....
Then for the moment just do the first two things and isolate the coefficient of the general term .