Question

The ninth term of the expansion ${\left(3x-\frac{1}{2x}\right)}^8$ is

• A. $\frac{1}{512x^9}$
• B. $\frac{-1}{512x^9}$
• C. $\frac{-1}{256x^8}$
• D. $\frac{1}{256x^8}$

Answer 1

The correct option is D

$\frac{1}{256x^8}$

Find the specified term in the expansion of the given expression

Given expression, ${\left(3x-\frac{1}{2x}\right)}^8$

Applying the binomial theorem expansion we get,

$T_9={}^8{C}_8{\left(3x\right)}^{8-8}{\left(\frac{-1}{2x}\right)}^8$

$=\frac{8!}{8!0!}\times 1\times \frac{1}{2^8{x}^8}$

$T_9=\frac{1}{256x^8}$

Hence, option $\left(D\right)$ is the correct answer.