Question

Does the expansion of ${(2x^2-\frac{1}{x})}^{20}$ contain any term involving $x^9?$

Answer 1

$(-1{)}^r{}^{20}{C}_r(2x^2{)}^{20-r}{\left(\frac{1}{x}\right)}^r$

$x^{40-2r}{x}^{-r}=x^9$

40-3r=9

31=3r

$r=\frac{31}{3}$

r cannot be in fraction

$\therefore$ There is no term involving?