Question

Write down and simplify $6^{th}$ term in the expansion of ${(\frac{2x}{3}+\frac{3y}{2})}^9$.

Answer 1

$T_6$ = ${}^9{C}_5{\left(\frac{2x}{3}\right)}^4.{\left(\frac{3y}{2}\right)}^5$

= $\frac{9\times 8\times 7\times 6\times 5}{5\times 4\times 3\times 2}\times \frac{2^4}{3^4}.\frac{3^5}{2^5}.x^4{y}^5$

= $3^3\times 7x^4{y}^5$

= $189x^4{y}^5$.