Question

Find the coefficient of $x^{32}$ in the expansion of ${(x^4-\frac{1}{x^3})}^{15}$:

• A. $1340$
• B. $1320$
• C. $1380$
• D. $1365$

Answer 1

The correct option is D $1365$

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

Collecting powers of $x$

$⟹60-4r-3r=-32$

$7r=28$

$r=4$

Coefficient of $x^{32}$

${=}^{15}{C}_4(-1{)}^{32}$

$=1365$