Question

If a+b+c=0, Then the value of (a+b) (b+c) (c+a) is

Answer 1

-abc is the answer

a+b =-c

b+c=-a

c+a=-b

Answer 2

if (a+b+c) then, we can write

(a+b)+c=0

or, (a+b) = -c                        ------(i)

similarly, (b+c) = -a       -----(ii)

           & (c+a) = -b      -----(iii)

SO,

(a+b)(b+c)(c+a) = (-c)×(-a)×(-b) = (-abc)