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To determine which expression is equivalent to \( x^3(2+y^5) \), we can distribute \( x^3 \) across the terms inside the parentheses.
Starting with:
\[ x^3(2+y^5) \]
We distribute \( x^3 \):
\[ = x^3 \cdot 2 + x^3 \cdot y^5 \]
This simplifies to:
\[ = 2x^3 + x^3y^5 \]
Now, let's compare this to the provided responses:
1. \( 2x^3 + y^5 \)
2. \( x^3 + 2 + y^5 \)
3. \( x^3 + x^3 + xy + xy + xy \)
4. \( 2x^3 + x^3y^5 \)
The expression \( 2x^3 + x^3y^5 \) matches our simplified expression perfectly.
Therefore, the correct answer is:
**2x^3 + x^3y^5**