If x, y, z are real numbers such that x+y+z=10 and xy+yz+zx=18, then what is the value of x^{3}+y^{3}+z^{3}-3xyz?

Explanation

First, find x^2+y^2+z^2 = (x+y+z)^2 - 2(xy+yz+zx) = 100 - 36 = 64. Then, use the identity x^3+y^3+z^3-3xyz = (x+y+z)[x^2+y^2+z^2 - (xy+yz+zx)] = 10 \times (64 - 18) = 460.

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