Coefficient of x^35 in Binomial Theorem Expansion

[xxwinexx]

Homework Statement

Find the coefficient of [PLAIN]http://webwork2.math.utah.edu/webwork2_files/tmp/equations/73/3e29a3b979c709dbb6c609c5a6ce891.png in the expansion of [PLAIN]http://webwork2.math.utah.edu/webwork2_files/tmp/equations/63/dcb58790e8122dce61b830977294091.png

Homework Equations

The Binomial Theorem

The Attempt at a Solution

This one is stumping me. I guess because in all of my previous problems, we didn't have any binomials which had parts raised to a higher power like (-3x)^5

Anyway, would my r in my nCr portion of the theorem be 15C34? Seeing as I'm attempting to find the term which has x^35th?

Typing that out, I think my question is actually, does the higher powers inside of the binomial have any effect on the theorem?

My attempt if this is true:

15C34(((-3a^5)^-19)-(3y^6)^34)

Typing that out looks horribly wrong. Some help please?

 

[Sethric]

Hrm, can't really understand what your attempt is saying.
Just picture the exponents differently:

$$x^{35} = (x^5)^7$$

$$y^{48} = (y^6)^8$$

Now you need to find the binomial coefficient for the $$a^7b^8$$ term in the expansion of$$(a+b)^{15}$$. Don't forget you will pick up some -3s. How many?