Question

If a + b + c = 0, then what is the value of (a + b-c)^3
+(c + a - b)^3 + (b + c - a)^3?
(A) a^3 + b^3+ c^3
(B) - 24abc
(C) a + b + c
(D) 24 abc​

Answer 1

Step-by-step explanation:

(a+b−c)3+(c+a−b)3+(b+c−a)3

=(−2c)3+(−2b)3+(−2a)3 As a+b+c=0

=−8(a3+b3+c3)−8(3abc−3abc)

=−8(a3+b3+c3−3abc)−24abc

=−4(a+b+c)((a−b)2+(b−c)2+(c−a)2)−24abc

= −24abc As a+b+c=0