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Given that $a + b + c = 0$ , what is $a^{3} + b^{3} + c^{3}$ equal to?

Class 9Algebraic IdentitiesPolynomials

A $(a + b + c)^{3}$
B $3 ab c$
C $ab c$
D $0$

Step-by-Step Solution

a^{3} + b^{3} + c^{3} - 3 ab c = (a + b + c) (a^{2} + b^{2} + c^{2} - ab - b c - c a)

. With

a + b + c = 0

the right side is 0, so the sum of cubes is 3

ab c

.

Answer: B)

3 ab c

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