Question

if a +b+c=0 then find the value of the above equation​

Answer 1

Answer:

-24abc

Step-by-step explanation:

Since a+b+c=0

a+b = -c

b+c = -a

a+c = -b

Put that into given equation

(a+b-c)³ + (c+a-b)³ + (b+c-a)³

(-c-c)³ + (-b-b)³ + (-a-a)³

(-2c)³ + (-2b)³ + (-2a)³

-8c³ - 8b³ - 8a³

-8(a³+b³+c³)

-8(3abc)        [∵ a³+b³+c³=3abc]

-24abc

Explanation for a³+b³+c³=3abc

a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-ab-bc-ca)

∵a+b+c=0

a³+b³+c³-3abc = 0

a³+b³+c³=3abc