2a(a+b-c)-2b(a-b-c)+2c(a-b+c)=

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