Find the coefficient of $x^2$ in the expansion of $(3x+1{)}^5$.

Step-by-step solution

1. Compute the general term: $T_{k+1}=\left(\genfrac{}{}{0ex}{}{5}{k}\right)(3x{)}^k(1{)}^{5-k}$.
2. Set $k=2$ for $x^2$.
3. Calculate $\left(\genfrac{}{}{0ex}{}{5}{2}\right)=10$.
4. Compute $(3x{)}^2=9x^2$.
5. Multiply: $10\times 9=90$.
6. Thus the coefficient of $x^2$ is $90$.

Concept tested: Coefficient of a term in binomial expansion

Published 16 October 2026 · How this solution was prepared and checked