Expand and simplify $(2\sqrt{7} + 1)(\sqrt{7} - 1) - (\sqrt{7} - 1)$.

First, notice that $(\sqrt{7} - 1)$ is a common factor:

$= (\sqrt{7} - 1)\bigl[(2\sqrt{7} + 1) - 1\bigr]$

$= (\sqrt{7} - 1)(2\sqrt{7})$

$= 2\sqrt{7} \cdot \sqrt{7} - 2\sqrt{7} \cdot 1$

$= 2 \cdot 7 - 2\sqrt{7}$

$= 14 - 2\sqrt{7}$