Simplify and factorize
(a+b+c)^2 - (a-b-c)^2 +4b^2 -4c^2

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Solution

=a²+b²+c²+2ab+2bc+2ca-(a²+b²+c²-2ab+2bc-2ca) +4b²-4c²
=4ab+4ca+4b²-4c²
=4(b²+ab-c²+ca)
=4[b(a+b)-c(c-a)]

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