Question

Find the middle term in the expansion ${(\frac{x}{a}+\frac{y}{b})}^6$.

Answer 1

Given expression,

${(\frac{x}{a}+\frac{y}{b})}^6$

No of terms will be $6+1=7$ terms

$\therefore$ middle term will be $4^{th}$ term

$t_4={}^6{C}_3{\left(\frac{x}{a}\right)}^3{\left(\frac{y}{b}\right)}^{6-3}$

$t_4=20\times \frac{x^3{y}^3}{a^3{b}^3}$ is the middle term.