Simplify

\[ (a+b+c)^2 + (a-b+c)^2 \]

Solution:

\[ (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca \]

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

\[ (a+b+c)^2 + (a-b+c)^2 \]

\[ = a^2+b^2+c^2+2ab+2bc+2ca \]

\[ + a^2+b^2+c^2-2ab-2bc+2ca \]

\[ = 2a^2+2b^2+2c^2+4ca \]

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