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Verify that x^(3)+y^(3)+z^(3)-3xyz=(1)/(...

Verify that `x^(3)+y^(3)+z^(3)-3xyz=(1)/(2)(x+y+z)[(x-y)^(2)+(y-z)^(2)+(z-x)^(2)]`

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To verify the identity \( x^3 + y^3 + z^3 - 3xyz = \frac{1}{2}(x+y+z)\left[(x-y)^2 + (y-z)^2 + (z-x)^2\right] \), we will start with the right-hand side (RHS) and simplify it to see if it equals the left-hand side (LHS). ### Step 1: Write down the RHS The right-hand side of the equation is: \[ \text{RHS} = \frac{1}{2}(x+y+z)\left[(x-y)^2 + (y-z)^2 + (z-x)^2\right] \] ...
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