Which expression is equivalent to x3(2+y5) ?(1 point)

Question

Responses

2x3+y5
2 x cubed plus y superscript 5 baseline

2x3+x3y5
2 x cubed plus x cubed y superscript 5 baseline

x3+2+y5
x cubed plus 2 plus y superscript 5 baseline

x3+x3+xy+xy+xy

Answer 1

To find an expression equivalent to \( x^3(2 + y^5) \), we can use the distributive property (also known as the distributive law of multiplication over addition):

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

This simplifies to:

\[ 2x^3 + x^3y^5 \]

Now, we can match this expression with the given responses:

1. 2x³ + y⁵: This is not equivalent because it does not include the \( x^3 \) term multiplied by \( y^5 \).
2. 2x³ + x³y⁵: This matches our derived expression.
3. x³ + 2 + y⁵: This is not equivalent because it suggests addition rather than multiplication and does not represent the original expression correctly.
4. x³ + x³ + xy + xy + xy: This simplifies to \( 2x^3 + 3xy \), which is also not equivalent to our expression.

Thus, the correct answer is:

2x³ + x³y⁵.