Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 2.$  Find the maximum value of
\[(x^2 - xy + y^2)(x^2 - xz + z^2)(y^2 - yz + z^2).\]
Question:
Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 2.$  Find the maximum value of
\[(x^2 - xy + y^2)(x^2 - xz + z^2)(y^2 - yz + z^2).\]
Answer:
Let's think step by step.

user
\frac{256}{243}
Let $x,$ $y,$ and $z$ be nonnegative real numbers such that $x + y + z = 2.$  Find the maximum value of
\[(x^2 - xy + y^2)(x^2 - xz + z^2)(y^2 - yz + z^2).\]
train