Find the coefficient of $x^{5}$ and $x^{- 15}$ in the expansion of ${(3 x^{2} - \frac{1}{3 x^{3}})}^{10}$ ?

Open in App

Solution

$T_{r + 1} =^{10} C_{r} 3^{10 - r} (- b)^{r} \cdot x^{20 - 2 r - 3 r}$
$∴ 20 - 5 r = 5$ or -15
$∴ r = 3$ or $r = 7$
$∴$ Coeff. of $x^{5}$ is $- 9720 b^{3}$ and that of $x^{- 15}$ is $- \frac{40}{27} b^{7}$

Suggest Corrections

Similar questions

x^{- 15}

(3 x^{2} - \frac{1}{3 x^{3}})^{10}

Find the coefficient of $x^{5}$ in the expansion of $(\frac{(1 + x)^{31}}{x})$

x^{5}

(1 - 3 x + 3 x^{2})^{- \frac{1}{2}}

x^{5}

(1 + 3 x - 2 x^{3})^{8}

x^{5}

\frac{1 + x^{2}}{1 + x}

| x | < 1

Join BYJU'S Learning Program