Simplify
\[ (a+b+c)^2 + (a-b+c)^2 + (a+b-c)^2 \]
Solution:
\[ (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca \]
\[ (a-b+c)^2 = a^2+b^2+c^2-2ab-2bc+2ca \]
\[ (a+b-c)^2 = a^2+b^2+c^2+2ab-2bc-2ca \]
\[ (a+b+c)^2 + (a-b+c)^2 + (a+b-c)^2 \]
\[ = 3a^2+3b^2+3c^2+2ab-2bc+2ca \]