Question

The coefficient of $x^3$ in $(2x-\frac{3}{x^2}{)}^9$ is

• A. $2^9{.3}^5$
• B. $2^8{.3}^5$
• C. $2^8{.3}^4$
• D. $2^9{.3}^4$

Answer 1

The correct option is D $2^9{.3}^4$

The general term is
$t_r{=}^9{C}_r.(-1{)}^{9-r}.(2x{)}^r.(\frac{3}{x^2}{)}^{9-r}$
If the power of $x$ in above general term should be $3$, we have,
$r-2(9-r)=3$ which gives $r=7$.
Putting this value of $r$ in the general term expression, we get the coefficient of $x^3$