Question

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

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

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

x3+x3+xy+xy+xy
x cubed plus x cubed plus x y plus x y plus x y

2x3+y5

Answer 1

The expression \( x^3(2 + y^5) \) can be simplified using the distributive property. This involves distributing \( x^3 \) to both terms inside the parentheses.

1. First, distribute \( x^3 \) to \( 2 \):
\[
x^3 \cdot 2 = 2x^3
\]

2. Then, distribute \( x^3 \) to \( y^5 \):
\[
x^3 \cdot y^5 = x^3y^5
\]

Putting these pieces together gives:
\[
x^3(2 + y^5) = 2x^3 + x^3y^5
\]

Now, looking at the response options:

- \( 2x^3 + x^3y^5 \): This matches our simplified expression.
- The other options do not match.

Therefore, the correct equivalent expression is:
**\( 2x^3 + x^3y^5 \)**.