Which expression is equivalent to x^3 (2 + y^5)?

Question

x^3 + 2 + y^5
x^3 + x^3 + xy + xy + xy
2x^3 + x^3y^5
2x^3 + y^5

Answer 1

To find an expression that is equivalent to \( x^3(2 + y^5) \), we can distribute \( x^3 \):

\[ x^3(2 + y^5) = x^3 \cdot 2 + x^3 \cdot y^5 = 2x^3 + x^3y^5 \]

Now, let's examine the given options:

1. \( x^3 + 2 + y^5 \)
2. \( x^3 + x^3 + xy + xy + xy \)
3. \( 2x^3 + x^3y^5 \)
4. \( 2x^3 + y^5 \)

The expression we derived, \( 2x^3 + x^3y^5 \), matches option 3.

So, the correct answer is:

\( 2x^3 + x^3y^5 \).