Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 3.$  Find the maximum value of
\[(xy + z)(xz + y).\]
Question:
Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 3.$  Find the maximum value of
\[(xy + z)(xz + y).\]
Answer:
Let's think step by step.

user
4
Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 3.$  Find the maximum value of
\[(xy + z)(xz + y).\]
train