Simplify
\[ (a+b+c)^2 – (a-b+c)^2 \]
Solution:
\[ (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca \]
\[ (a-b+c)^2 = a^2+b^2+c^2-2ab-2bc+2ca \]
\[ (a+b+c)^2 – (a-b+c)^2 \]
\[ = a^2+b^2+c^2+2ab+2bc+2ca \]
\[ – (a^2+b^2+c^2-2ab-2bc+2ca) \]
\[ = 4ab+4bc \]
\[ = 4b(a+c) \]