Question

Find the $4^{th}$ term from the end in the expansion of ${(\frac{x^3}{2}-\frac{2}{x^2})}^7$

Answer 1

$4^{th}$ term from the end in the expansion of ${(\frac{x^3}{2}-\frac{2}{x^2})}^7$

$=4^{th}$ term from the end in the expansion of ${(-\frac{2}{x^2}+\frac{x^3}{2})}^7$

$=T_4=T_{3+1}{=}^7{C}_3{\left(\frac{-2}{x^2}\right)}^{7-3}{\left(\frac{x^3}{2}\right)}^3$

$=\frac{\mathrm{7.6.5}}{\mathrm{1.2.3}}\frac{2^4}{x^8}.\frac{x^9}{2^3}=70x$