Question

Find the middle term in the expansion of
${(\frac{2x}{3}-\frac{3}{2x})}^6$

Answer 1

Total terms $=6+1=7$ terms

Middle terms $=\frac{7+1}{2}=4^{th}$ term

$T_4={}^6{C}_3{\left(\frac{2x}{3}\right)}^3{\left(\frac{-3}{2x}\right)}^3$

$=\frac{6!}{3!3!}\times (-1{)}^3=\frac{-6\times 5\times 4}{3\times 2}$

$=-20$.