## (Math Quiz 10 – CT) In the expansion ({left( {2x – 5y} right)^8}), the coefficient of the containing term ({x^5}. {y^3}) is:

• Question:

In the expansion $${\left( {2x – 5y} \right)^8}$$, the coefficient of the term containing $${x^5}.{y^3}$$ is:

Reference explanation:

$$\begin{array}{l} {T_{k + 1}} = {\left( { – 1} \right)^k}C_8^k. {\left( {2x} \right)^{8 – k}}{\left( {5y} \right)^k}\\ = {\left( { – 1} \right)^k}C_8^k{.2^{8 – k}}{5^k}. {x^{8 – k}}. {y^k} \end{array}$$
Requires the problem to occur when. Then the coefficient of the term containing $${x^5}.{y^3}$$ is:−22400