The coefficient of x^5 in the expansion of (2x^3-13x^2)^5 is :

Question

The coefficient of ${x}^{5}$ in the expansion of ${(2{x}^{3}-\frac{1}{3{x}^{2}})}^{5}$ is :

Accepted Answer

Given, $$\left(2 x^{3}-\frac{1}{3 x^{2}}\right)^{5}$$

General term,

$$
\begin{aligned}
& T_{r+1}={ }^5 C_r\left(2 x^3\right)^{5-r}\left(\frac{-1}{3 x^2}\right)^r={ }^5 C_r \frac{(2)^{5-r}}{(-3)^r}(x)^{15-5 r} \\
& \therefore 15-5 \mathrm{r}=5 \\
& \therefore \mathrm{r}=2 \\
& T_3=10\left(\frac{8}{9}\right) x^5
\end{aligned}
$$

So, coefficient is $\frac{80}{9}$.

Solutions · 1