Question

Write down and simplify:
The 7th term of ${(\frac{4x}{5}-\frac{5}{2x})}^9$

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 $7^{th}$ term in the expansion of ${(\frac{4x}{5}-\frac{5}{2x})}^9$ is ${}^9{C}_6\frac{(4x{)}^3}{5^3}\frac{(-5{)}^6}{(2x{)}^6}$ which equals $\frac{10500}{x^3}$