\[(a + b + c)^{2} - (a - b - c)^{2} =\]
\[= (a + b + c - a + b + c) \cdot 2a =\]
\[= 2a(2b + 2c) = 2 \cdot 2a(b + c) =\]
\[= 4a(b + c).\]