![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} - 3xyz = \frac{1}{2} (x + y + z)(x - {y}^{2} ) + (y - {z}^{2} ) + (z - {x}^{2} )](https://tex.z-dn.net/?f=verify+++%5C%3A++%5C%3A++that+%5C%3A++%5C%3A++%5C%3A++%5C%3A+%5C%3A++%7Bx%7D%5E%7B3%7D++%2B++%7By%7D%5E%7B3%7D++%2B++%7Bz%7D%5E%7B3%7D++-+3xyz+%3D+++%5Cfrac%7B1%7D%7B2%7D++%28x+%2B+y+%2B+z%29%28x+-++%7By%7D%5E%7B2%7D++%29+%2B+%28y+-+++%7Bz%7D%5E%7B2%7D+%29+%2B+%28z+-++%7Bx%7D%5E%7B2%7D+%29)
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