## (Math Quiz 10 – CT) In the expansion ({left( {2x – 1} right)^{10}}), the coefficient of the term containing x 8 x8 is:

• Question:

In the expansion $${\left( {2x – 1} \right)^{10}}$$, the coefficient of the term containing x 8 x8 is:

Reference explanation:

The general term in the above expansion is

$${T_{k + 1}} = C_{10}^k{.2^{10 – k}} {x^{10 – k}} {\left( { – 1} \right)^ k}$$

Requires the problem to occur when

$$10 – k = 8 \Leftrightarrow k = 2$$

Then the coefficient of the term containing $${x^8}$$ is: $$C_{10}^2{.2^8} = 11520$$.