<s>[INST] Algebraic identities Given that $$a+b+c=2$$ and $$ab+bc+ca=1$$
Then the value of 
$$(a+b)^2+(b+c)^2+(c+a)^2$$ is how much?

Attempt:
Tried expanding the expression. Thought the expanded version would contain a term from the expression of $a^3+b^3+c^3-3abc$, but its not the case. 
 [/INST] $(a+b)^2 + (b+c)^2 + (a+c)^2=a^2+b^2+c^2+2ab+2bc+2ac=2(a^2+b^2+c^2)+2(ab+bc+ac)=2(a^2+b^2+c^2)+2 \cdot 1=2((a+b+c)^2-2(ab+bc+ac))=2  \cdot (2)+2=6$
</s>