Question

The middle term in the expansion of ${(\frac{x}{y}+\frac{y}{x})}^8$ is.

• A. ${}^8{\text{C}}_5$
• B. ${}^8{\text{C}}_6$
• C. ${}^8{\text{C}}_4$
• D. ${}^8{\text{C}}_2$

Answer 1

The correct option is C ${}^8{\text{C}}_4$

The middle term of the expression

${(\frac{x}{y}+\frac{y}{x})}^8$

There are $9$ terms in the above expansion.

Hence the middle term will be the $5^{th}$ term

$T_5=C_4^8{\left(\frac{x}{y}\right)}^4{\left(\frac{y}{x}\right)}^4=$${}^8{\text{C}}_4$