Question

Find the coefficient of $x^{-17}$ in the expansion of ${(x^4-\frac{1}{x^3})}^{15}$:

• A. $1200$
• B. $-1331$
• C. $-1365$
• D. $-2016$

Answer 1

The correct option is C $-1365$

$T_{r+1}{=}^{15}{C}_r\left(x^4{)}^{15-r}\right(-1{)}^r(x^{-3}{)}^{-r}$

Collecting powers of $x$

$⟹60-4r-3r=-17$

$7r=77$

$r=11$

Coefficient of $x^{-17}$

${=}^{15}{C}_{11}(-1{)}^{1}1$

$-1365$