\[(x + 1)^{2} \cdot (x - 1)^{2} =\]
\[= \left( (x + 1)(x - 1) \right)^{2} = \left( x^{2} - 1 \right)^{2} =\]
\[= \left( x^{2} - 1 \right)\left( x^{2} - 1 \right).\]