Question

a+b+c=0 then (a+b) (b+c) (c+a) =?​

Answer 1

(a+b)(b+c)(c+a) = (ab+ac+b^2+bc)(c+a)

= abc+ac^2+b^2c+bc^2+a^2b+a^2c+ab^2+abc

= ab(a+b+c)+cb(a+b+c)+ac(a+c).

= 0 + 0 -abc.

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Answer 2

Heya!!

a + b + c = 0

a = - ( b + c )

b = - ( a + c )

c = - ( a + b )

So, ( a + b ) × ( b + c ) × ( c + d ) =

( - c ) × ( - a ) × ( - b )

= -abc