Question

Find $7^{th}$ term of ${(\frac{4x}{5}-\frac{5}{2x})}^9$

• A. $\frac{10050}{x^3}$
  
• B. $\frac{10500}{x^3}$
• C. $\frac{1050}{x^3}$
• D. $\frac{1000}{x^3}$

Answer 1

Answer: (B)

$\frac{10500}{x^3}$

$7^{th}$ term of ${(\frac{4x}{5}-\frac{5}{2x})}^9$
$T_{6+1}{=}^9{\text{C}}_6{\left(\frac{4x}{5}\right)}^{9-6}{(-\frac{5}{2x})}^6$
$=\frac{9!}{3!6!}{\left(\frac{4x}{5}\right)}^3{\left(\frac{5}{2x}\right)}^6=\frac{10500}{x^3}$