Verify that x 3 - y 3 - z 2 -3x y 2 - 1 2 x-y-z - zx-y 2 - y-z 2 - z-x 2 -

x^3 + y^3 + z^2 3xyz =(x+y+z)(x^2+y^2+z^2 xy yz zx) = 12(x + y + z)(2x^2 + 2y^2 + 2z^2 2xy 2yz 2zx) = 12(x + y + z)(x^2 + y^2 2xy ...

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Simplification of an Expression

Verify that ...

Question

Verify that $x^{3} + y^{3} + z^{2} - 3 x y^{2} = \frac{1}{2} (x + y + z) [{(z x - y)}^{2} + {(y - z)}^{2} + {(z - x)}^{2}]$

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Verify that $x^{3}$ + $y^{3}$ + $z^{3}$ - 3xyz = $\frac{1}{2}$ ((x + y + z)[ ${(x - y)}^{2}$ + ${(y - z)}^{2}$ + ${(z - x)}^{2}$ ]

Verify that : $x^{3} + y^{3} + z^{3} - 3 x y z = \frac{1}{2} (x + y + z) [{(x - y)}^{2} + {(y - z)}^{2} + {(z - x)}^{2})]$

x^{3} + y^{3} + z^{3} - 3 x y z = \frac{1}{2} (x + y + z) [(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) [(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) [(x - y)^{2} + (y - z)^{2} + (z - x)^{2}]

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