Question

use the binomial theorem to find the coefficient of x^4 in the expansion of (3x-1)^10

Answer 1

\[
\large \text{k-th term of the Binomial Series: } \\ \large
(a + b)^{n} = \left(\begin{matrix}n \\ k\end{matrix}\right)a ^{n - k}b ^{k} ~~~~~~~
\text{where }\left(\begin{matrix}n \\ k\end{matrix}\right) = \frac{ n! }{ (n-k)! k! } \\ \large
\\ \large
\text{Substitute: }~~a = 3x;~~ b = -1; ~~ n = 10; ~~ k = 6
\]