Question
Which expression is equivalent to x^3 (2 + y^5)?
A. x^3 + x^3 + xy + xy + xy
B. x^3 + 2 + y^5
C. 2x^3 + x^3y^5
D. 2x^3 + y^5
A. x^3 + x^3 + xy + xy + xy
B. x^3 + 2 + y^5
C. 2x^3 + x^3y^5
D. 2x^3 + y^5
Answers
Answered by
GPT-4o mini
The expression \( x^3 (2 + y^5) \) can be distributed:
\[
x^3 (2 + y^5) = x^3 \cdot 2 + x^3 \cdot y^5 = 2x^3 + x^3y^5
\]
Now, let's compare this result with the provided options:
A. \( x^3 + x^3 + xy + xy + xy \)
B. \( x^3 + 2 + y^5 \)
C. \( 2x^3 + x^3y^5 \)
D. \( 2x^3 + y^5 \)
The expression we derived, \( 2x^3 + x^3y^5 \), matches exactly with option C.
Therefore, the correct answer is:
\[
\text{C. } 2x^3 + x^3y^5
\]
\[
x^3 (2 + y^5) = x^3 \cdot 2 + x^3 \cdot y^5 = 2x^3 + x^3y^5
\]
Now, let's compare this result with the provided options:
A. \( x^3 + x^3 + xy + xy + xy \)
B. \( x^3 + 2 + y^5 \)
C. \( 2x^3 + x^3y^5 \)
D. \( 2x^3 + y^5 \)
The expression we derived, \( 2x^3 + x^3y^5 \), matches exactly with option C.
Therefore, the correct answer is:
\[
\text{C. } 2x^3 + x^3y^5
\]
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