\(=\left(a+b\right)^2+\left(b+c\right)^2+\left(c+a\right)^2\)
(a + b + c)2 + a2 + b2 + c2
=a2+b2+c2+2ab+2ac+2bc+a2+b2+c2
=(a2+2ab+b2)+(b2+2bc+c2)+(a2+2ac+c2)
=(a+b)2+(b+c)2+(a+c)2
\(\left(a+b+c\right)^2+a^2+b^2+c^2\)
\(=\left(a^2+2ab+b^2\right)+\left(b^2+2bc+c^2\right)+\left(a^2+2ac+c^2\right)\)
\(=\left(a+b\right)^2+\left(b+c\right)^2+\left(a+c\right)^2\)