Hello, delso!
They used the Distributive Property.
$\displaystyle (\overbrace{z^2+\tfrac{1}{z^2}}^a + \overbrace{2}^b)(\overbrace{z^2-\tfrac{1}{z^2}}^c) \;=\;\overbrace{\left(x^2+\tfrac{1}{z^2}\right)}^a \overbrace{\left(z^2-\tfrac{1}{z^2}\right)}^c + \overbrace{2}^b \overbrace{\left(z^2 - \tfrac{1}{z^2}\right)}^c$