Question

simplify:(a+b+c)^2+(a-b+c)^2 +(a+b-c)^2.​

Answer 1

Step-by-step explanation:

(a+b+c)(a+b+c)+(a-b+c)(a-b+c)+(a+b-c)(a+b-c)

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

=a²+ab+ac+ab+b²+bc+ac+bc+c²+a²-ab+ac-ab+b²-bc+ac-bc+c²+a²+ab-ac+ab+b²-bc-ac-bc+c²

=3a²+3b²+3c²+2ab+2ac-2bc