Question

Write down and simplify:
The 4th term of ${(\frac{a}{3}+9b)}^{10}$.

Answer 1

The $r^{th}$ term in expansion of $(a+x{)}^n$ is given by ${}^n{C}_{r-1}{a}^{n+1-r}{x}^{r-1}$

$\therefore$ the $4^{th}$ term in the expansion of ${(\frac{a}{3}+9b)}^{10}$ is ${}^{10}{C}_3\frac{a^7}{3^7}{9}^3{b}^3$ which equals $40a^7{b}^3$