Answer
$3360$
Work Step by Step
We are given the expression:
$\left(x-\dfrac{2}{\sqrt x}\right)^{10}$
The term $T_{k+1}$ of the expansion of $(a+b)^n$ is:
$T_{k+1}=\binom{n}{k}a^{n-k}b^r$
We have:
$T_{k+1}=\binom{10}{k}x^{10-k}(-2x^{-1/2})^k=(-2)^k\binom{10}{k}x^{10-k-0.5k}=(-2)^k\binom{10}{k}x^{10-1.5k}$
Determine $k$ so that the term contains $x^4$:
$10-1.5k=4$
$6=1.5k$
$k=4$
Determine the coefficient of $x^4$:
$(-2)^4\binom{10}{4}=16\cdot\dfrac{10!}{4!6!}=3360$
