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Mathematics
Problem
12. Verify that
x
3
+
y
3
+
z
3
−
3
x
y
z
=
1
2
(
x
+
y
+
z
)
[
(
x
−
y
)
2
+
(
y
−
z
)
2
+
(
z
−
x
)
2
]
x^{3}+y^{3}+z^{3}-3 x y z=\frac{1}{2}(x+y+z)\left[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}\right]
x
3
+
y
3
+
z
3
−
3
x
y
z
=
2
1
(
x
+
y
+
z
)
[
(
x
−
y
)
2
+
(
y
−
z
)
2
+
(
z
−
x
)
2
]
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