If a+b+c=0, then the value of a^{3}+b^{3}+c^{ | vedclass

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(B) We know the algebraic identity:$a^{3}+b^{3}+c^{3}-3abc = (a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)$Given that $a+b+c=0,$Substituting this value into the

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$3abc$

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(B) We know the algebraic identity:$a^{3}+b^{3}+c^{3}-3abc = (a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)$Given that $a+b+c=0,$Substituting this value into the identity:$a^{3}+b^{3}+c^{3}-3abc = (0)(a^{2}+b^{2}+c^{2}-ab-bc-ca)$$a^{3}+b^{3}+c^{3}-3abc = 0$Therefore,$a^{3}+b^{3}+c^{3} = 3abc.$Thus,the correct option is $(B)$.

If $a+b+c=0,$ then the value of $a^{3}+b^{3}+c^{3}$ is equal to

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