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If x+y+z=0 show that x^3+y^3+z^3=3x y z...

If `x+y+z=0` show that `x^3+y^3+z^3=3x y z`.

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To prove that if \( x + y + z = 0 \), then \( x^3 + y^3 + z^3 = 3xyz \), we can use the identity for the sum of cubes. ### Step-by-step Solution: 1. **Recall the identity**: The identity we will use is: \[ x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx) ...
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