Which expression is equivalent to x^3(2+y^5)?(1 point)

Question

Responses

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

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

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

x3+x3+xy+xy+xy

Answer 1

To simplify the expression \( x^3(2+y^5) \), we distribute \( x^3 \) to both terms inside the parentheses:

1. Distributing to the first term: \[ x^3 \cdot 2 = 2x^3 \]

2. Distributing to the second term: \[ x^3 \cdot y^5 = x^3 y^5 \]

Putting it all together, we have: \[ x^3(2+y^5) = 2x^3 + x^3 y^5 \]

Now, let's analyze the provided options:

1. 2x3 + x3y5: This is \( 2x^3 + x^3y^5 \) - this matches our result.
2. x3 + 2 + y5: This simplifies to \( x^3 + 2 + y^5 \) - this does not match.
3. 2x3 + y5: This simplifies to \( 2x^3 + y^5 \) - this does not match.
4. x3 + x3 + xy + xy + xy: This simplifies to \( 2x^3 + 3xy \) - this does not match.

The correct expression equivalent to \( x^3(2+y^5) \) is:

2x3 + x3y5.