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. 

If you just want the value of expression $(a+b)^2 + (b+c)^2 + (a+c)^2$than set the vale of  $a=0$, $b=1$ and $c=1$ (these satisfy the required conditions ) and you are going to get the answer.
$$(1)^2 + (2)^2 + (1)^2 = 6$$
