Question

If a+b+c=0 .Then find the factor of the expression (a+b)³+(b+c)³+(a+c)³​

Answer 1

Step-by-step explanation:

(a+b)³+(b+c)³+(a+c)³

a³+b³+3ab(a+b)+b³+c³+3bc(b+c)+a³+c³+3ac(a+c)

2(a³+b³+c³)+3(a²b+b²a+b²c+c²b+a²c+c²a)

Then,

a + b + c = 0

a + b = - c -- (I)

(a + b)^3 = (- c)^3

a^3 + b^3 + 3ab (a + b) = - c^3

from equation (I) a + b = - c

a^3 + b^3 + 3ab (- c) = - c^3

a^3 + b^3 - 3abc = - c^3

a^3 + b^3 + c^3 = 3abc

Hence,

a^3 + b^3 + c^3 ‘not equal’ 0

but,

a^3 + b^3 + c^3 ‘equal’ 3abc