Question

Find the coefficient of x^6 in the binomial expansion of (2x+3)^9.

Answer 1

Binomial theorem:
\[(a+b)^n=\sum_{k=0}^n\binom nk a^{n-k} b^k\]In regards to your problem:
\[(2x+3)^9=\sum_{k=0}^n\binom 9k (2x)^{9-k} 3^k\]You have an instance of \(x^6\) when \(k=3\), since \(9-3=6\) gives a degree of \(6\) on the \(x\) term.

So when \(k=3\), the resulting term is \(\displaystyle \binom 93 (2x)^6 3^3\). You should be able to figure out the coefficient from there.