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To determine which expression is equivalent to \( x^3(2 + y^5) \), we can distribute \( x^3 \) into the parentheses:
\[
x^3(2 + y^5) = x^3 \cdot 2 + x^3 \cdot y^5 = 2x^3 + x^3y^5.
\]
Now, let's review the provided responses:
1. \( 2x^3 + y^5 \)
2. \( x^3 + x^3 + xy + xy + xy \)
3. \( 2x^3 + x^3y^5 \)
4. \( x^3 + 2 + y^5 \)
The correct expression that matches our simplified result \( 2x^3 + x^3y^5 \) is option 3:
**3) \( 2x^3 + x^3y^5 \)**.
This is the equivalent expression.