Rewrite $ 121x^{2}-100 $ as:
$$ 121x^{2}-100 = (11x)^2 - (10)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 11x $ and $ II = 10 $ , we have:
$$ 121x^{2}-100 = (11x)^2 - (10)^2 = ( 11x-10 ) ( 11x+10 ) $$