Which expression is equivalent to x3(2+y5)

Question

?(1 point)
Responses

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

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

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

2x3+y5

Answer 1

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

Let's distribute \( x^3 \) to both terms inside the parentheses:

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

This results in:

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

Now let's check against the provided options:

1. \( x^3 + x^3 + xy + xy + xy \) - This is not correct.
2. \( x^3 + 2 + y^5 \) - This is not correct.
3. \( 2x^3 + x^3y^5 \) - This is the correct option.
4. \( 2x^3 + y^5 \) - This is not correct.

Thus, the correct answer is:

2x^3 + x^3y^5.