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If $x + y + z = 0$ , then $x^{3} + y^{3} + z^{3}$ is equal to:

Competition practiceAlgebra

A0
B $x yz$
C $3 x yz$
D $x^{3} y^{3} z^{3}$

Step-by-Step Solution

The identity

x^{3} + y^{3} + z^{3} - 3 x yz = (x + y + z) (x^{2} + y^{2} + z^{2} - x y - yz - z x)

. When

x + y + z = 0

the right side is 0, so

x^{3} + y^{3} + z^{3} = 3 x yz

.

Answer: C)

3 x yz

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