Binomial Theorem

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Homework Statement


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


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?
 
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Answers and Replies

  • #2
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Hrm, can't really understand what your attempt is saying.
Just picture the exponents differently:

[tex]x^{35} = (x^5)^7[/tex]

[tex]y^{48} = (y^6)^8[/tex]

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

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