Rewrite $ q^{2}-121 $ as:
$$ q^{2}-121 = (q)^2 - (11)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = q $ and $ II = 11 $ , we have:
$$ q^{2}-121 = (q)^2 - (11)^2 = ( q-11 ) ( q+11 ) $$