Question

Write the middle terms in the expansion of ${(\frac{3x}{7}-2y)}^{10}$.

Answer 1

Fact: If $n$ is even number then then middle term in the expansion of $(x+y{)}^n$ will be ${}^n{C}_{\frac{n}{2}}{x}^{\frac{n}{2}}{y}^{\frac{n}{2}}$

So middle term in the expansion of

${(\frac{3x}{7}-2y)}^{10}$ is ${}^{10}{C}_5{\left(\frac{3x}{7}\right)}^5(-2y{)}^5$ $={\left(\frac{6}{7}\right)}^5$ ${}^{10}{C}_5(-xy{)}^5$