\[3x^{2} + 12xy + 12y^{2} =\]
\[= 3 \cdot \left( x^{2} + 4xy + 4y^{2} \right) = 3 \cdot (x + 2y)^{2} =\]
\[= 3 \cdot (x + 2y)(x + 2y)\]