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 $\left(2x^3-\dfrac{1}{3x^2}\right)^5$ is

Accepted Answer

$$T_{r+1}=\binom5r\left(-\frac1{3x^2}\right)^r(2x^3)^{5-r}=\binom5r(-1)^r3^{-r}2^{5-r}x^{15-5r}$$

For $x^5$: $15-5r=5\Rightarrow r=2$.

$$\binom52(-1)^23^{-2}2^3=10\times\frac19\times8=\frac{80}{9}$$

Solutions · 1