## (Math Quiz 10 – CT) In the expansion ({left( {3x – y} right)^7}), the term containing ({x^4}{y^3}) is:

• Question:

In the expansion $${\left( {3x – y} \right)^7}$$, the term containing $${x^4}{y^3}$$ is:

Reference explanation:

The general term in the above expansion is

$${T_{k + 1}} = C_7^k{.3^{7 – k}}{x^{7 – k}}. {\left( { – 1} \right)^k}. { y^k}$$

Ask the problem to occur when k = 3 .

Then the coefficient of the term containing $${x^4}.{y^3}$$ is:

$$– C_7^3{.3^4}. {x^4}. {y^3} = – 2835. {x^4}.y$$