Question

(a+b)(b+c)(a+c)+abc; если a+b+c=0

Answer 1

А=-b-c
(-b-c+b)(b+c)(-b-c+c)+(-b-c)*bc=-c(b+c)(-b)-b^2c-c^2b=cb(b+c)-b^2c-c^2b=b^2c+bc^2-b^2c-bc^2=0

Answer 2

To simplify the expression (a+b)(b+c)(a+c)+abc when a+b+c=0, we can make use of the fact that a+b+c equals zero. Let's proceed with the simplification step by step:

Given: a+b+c = 0

1. Substitute c = -(a+b) into the expression: (a+b)(b+c)(a+c)+abc = (a+b)(b+(-(a+b)))(a+(-(a+b)))+ab(-(a+b)) = (a+b)(b-a-b)(a-a-b)-ab(a+b) = (a+b)(-a)(-b)-ab(a+b) = -ab(a+b) - ab(a+b) = -2ab(a+b)

So, the simplified expression is -2ab(a+b) when a+b+c=0.