## (Math Quiz 10 – CT) In the expansion ({left( {x + frac{2}{{sqrt x }}} right)^6}), the coefficient of ({x^3},left( {x) > 0} right)) is:

• Question:

In the expansion $${\left( {x + \frac{2}{{\sqrt x }}} \right)^6}$$, the coefficient of $${x^3},\left( {x) > 0} \right)$$ is:

Reference explanation:

The general term in the above expansion is

$${T_{k + 1}} = C_6^k. {x^{6 – k}}{2^k}. {x^{ – \frac{1}{2}k}}$$

Requires the problem to occur when

$$6 – k – \frac{1}{2}k = 3 \Leftrightarrow k = 3$$

Then the coefficient of x3 is: $$C_6^3{.2^3} = 160$$.