Question

Write down and simplify:
The 5th term of ${(2a-\frac{b}{3})}^8$.

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 $5^{th}$ term in the expansion of ${(2a-\frac{b}{3})}^8$ is ${}^8{C}_4(2a{)}^4\frac{(-b{)}^4}{3^4}$ which equals $\frac{1120}{81}{a}^4{b}^4$