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Mathematics
Problem
If the expression
x
3
+
y
3
+
z
3
−
3
x
y
z
x^3 + y^3 + z^3 - 3xyz
x
3
+
y
3
+
z
3
−
3
x
y
z
is equal to 189, and
x
+
y
+
z
=
9
x + y + z = 9
x
+
y
+
z
=
9
, what is the value of
(
x
−
y
)
2
+
(
y
−
z
)
2
+
(
z
−
x
)
2
(x - y)^2 + (y - z)^2 + (z - x)^2
(
x
−
y
)
2
+
(
y
−
z
)
2
+
(
z
−
x
)
2
?
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