Question

In the expansion of ${(x^3-\frac{1}{x^2})}^{15}$,the constant term is

• A. ${}^{15}{\text{C}}_6$
• B. $0$
• C. ${-}^{15}{\text{C}}_9$
• D. $1$

Answer 1

The correct option is C ${-}^{15}{\text{C}}_9$

$T_{r+1}=(-1{)}^r{}^{15}{C}_r{x}^{45-5r}$
Hence the term independent of x will be given by
$45-5r=0$
$5r=45$
$r=9$
$T_{10}=-{}^{15}{C}_9$
$=-{}^{15}{C}_6$