Question

Question on Binomial theorem:
How to find the specific term that contains b^(some specific exponent) in (a+b)^n? I don't know if I wrote it right. But that's what the problems generally look like.

Answer 1

Here's one example. Find the term that contains y^8 in the binomial expansion of (2x+y^2)^6

Answer 2

The coefficient of the \(r^{th}\) term of of the expansion of \((a+b)^n\) is \((^n_r)=\frac{n!}{(n-r)!r!}\).
The \(r^{th}\) term is therefore \((^n_r)=\frac{n!}{(n-r)!r!}a^rb^{n-r}\)
For the above example, \(a=2x, b=y^2, n=6, r=4\) (because \((y^2)^4=y^8\).

Answer 3

OOOOHHHH How could I forget xD

Answer 4

Thanks a bunch.

Answer 5

You're welcome! :)