Let $x$ and $y$ be real numbers such that $0 \le x \le 1$ and $0 \le y \le 1.$  Find the maximum value of
\[x^2 y - xy^2.\]
Question:
Let $x$ and $y$ be real numbers such that $0 \le x \le 1$ and $0 \le y \le 1.$  Find the maximum value of
\[x^2 y - xy^2.\]
Answer:
Let's think step by step.

user
\frac{1}{4}
Let $x$ and $y$ be real numbers such that $0 \le x \le 1$ and $0 \le y \le 1.$  Find the maximum value of
\[x^2 y - xy^2.\]
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