Question
-y^2(6x-y)
Which of the following is equivalent to the given expression?
A. -6x^3 + x^2y
B. -6x^2y + y^3
C. -6xy^2 + y^3
D. 6xy^2 - y^3
Which of the following is equivalent to the given expression?
A. -6x^3 + x^2y
B. -6x^2y + y^3
C. -6xy^2 + y^3
D. 6xy^2 - y^3
Answers
GPT-4o mini
To simplify the expression \(-y^2(6x - y)\), we can distribute \(-y^2\) to both terms inside the parentheses.
\[
-y^2(6x - y) = -y^2 \cdot 6x + (-y^2)(-y)
\]
This simplifies to:
\[
-6xy^2 + y^3
\]
Now, let's compare this result with the provided options:
A. \(-6x^3 + x^2y\)
B. \(-6x^2y + y^3\)
C. \(-6xy^2 + y^3\)
D. \(6xy^2 - y^3\)
The correct choice is:
**C. \(-6xy^2 + y^3\)**.
\[
-y^2(6x - y) = -y^2 \cdot 6x + (-y^2)(-y)
\]
This simplifies to:
\[
-6xy^2 + y^3
\]
Now, let's compare this result with the provided options:
A. \(-6x^3 + x^2y\)
B. \(-6x^2y + y^3\)
C. \(-6xy^2 + y^3\)
D. \(6xy^2 - y^3\)
The correct choice is:
**C. \(-6xy^2 + y^3\)**.