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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 follow these steps: ### Step 1: Use the identity for the sum of cubes We start with the identity: \[ x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx) \] ...
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