Question

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

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

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

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

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

Answer 1

The expression given is \( x^3(2 + y^5) \). To find an equivalent expression, we can distribute \( x^3 \) to both terms inside the parentheses:

1. \( x^3 \cdot 2 = 2x^3 \)
2. \( x^3 \cdot y^5 = x^3y^5 \)

Putting it together, we get:

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

Now, let's consider the options given:

1. **2x3+y5** - This option is simply \( 2x^3 + y^5 \), which is not equivalent.
2. **x3+x3+xy+xy+xy** - This does not match the original expression.
3. **2x3+x3y5** - This matches our derived expression \( 2x^3 + x^3y^5 \).
4. **x3+2+y5** - This is not equivalent to the original expression.

Thus, the correct response is:

**2x3+x3y5** (which is the same as \( 2x^3 + x^3y^5 \)).