Question

verify (a+b)^2=a^2+b^2+b^2+2ab+2bc+2ca

Answer 1

It is not $(a+b) ^{2}$. It is $(a+b+c) ^{2}$
Now we will prove this.
(a+b+c)(a+b+c)= a(a+b+c)+b(a+b+c)+c(a+b+c)=a^2+ab+ac+ab+b^2+bc+ac+bc+c^2
⇒a^2+b^2+c^2+2ab+2bc+2ca