<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] Hint:
Express
 $S_2=a^2+b^2+c^2$  in function of $s=a+b+c$ and $\sigma=ab+bc+ca$ from the algebraic identity for $(a+b+c)^2$.
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