Find the containing `x^(3)` in the expansion of `(2y-x^((1)/(2)))^(10)`

Explanation

To find the term containing \( x^3 \) in the expansion of \( (2y - x^{\frac{1}{2}})^{10} \), we can follow these steps:

### Step 1: Identify the general term in the binomial expansion
The general term \( T_r \) in the expansion of \( (a + b)^n \) is given by:
\[ T_{r+1} = \binom{n}{r} a^{n-r} b^r \]
In our case, \( a = 2y \), \( b = -x^{\frac{1}{2}} \), and \( n = 10 \). Therefore, the general term becomes:
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