Question

which expression is equivalent to x^3 (2 + y^5)
A. 2x^3 + y^5
B. x^3 + 2 + y^5
C. 2x^3 + x^3y^5
D. x^3 + x^3 + xy + xy + xy

Answer 1

To simplify the expression \( x^3 (2 + y^5) \), we apply the distributive property:

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

So, the expression \( x^3 (2 + y^5) \) simplifies to \( 2x^3 + x^3y^5 \).

Now, we can compare this with the options provided:

A. \( 2x^3 + y^5 \) – not equivalent.
B. \( x^3 + 2 + y^5 \) – not equivalent.
C. \( 2x^3 + x^3y^5 \) – **this is equivalent**.
D. \( x^3 + x^3 + xy + xy + xy \) – not equivalent.

The correct answer is **C. \( 2x^3 + x^3y^5 \)**.