$\text{a)}\left(x-1\right)\left(x+1\right)=x^2+1x-1x-1=x^2-1$

$\text{b)}\left(1+3ab\right)\left(1-3ab\right)=1-3ab+3ab-9a^2{b}^2=1-9a^2{b}^2$

$\text{c)}\left(1-\sqrt{2}\right)\left(1+\sqrt{2}\right)=1+1\sqrt{2}-1\sqrt{-}{\sqrt{2}}^2=1-2=-1$

$\text{d)}\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)={\sqrt{5}}^2\mp 2\sqrt{5}-2\sqrt{5}-4=5-4=1$

$\text{e)}\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)={\sqrt{7}}^2-\sqrt{21}+\sqrt{21}-{\sqrt{3}}^2=7-3=4$

$\text{f)}\left(a+b\right)\left(a-b\right)=a^2-ab+ba-b^2=a^2-b^2$