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a+b+c=0 a^3+b^3+c^3=?
We use the identity that a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2 + b^2 + c^2 - ab - bc - ca) Now, if a+b+c = 0, the RHS becomes zero, thus the LHS is also zero => a^3 + b^3 + c^3 - 3abc = 0 => a^3 + b^3 + c^3 = 3abc
We use the identity that
a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2 + b^2 + c^2 - ab - bc - ca)
Now, if a+b+c = 0, the RHS becomes zero, thus the LHS is also zero
=> a^3 + b^3 + c^3 - 3abc = 0
=> a^3 + b^3 + c^3 = 3abc
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