Rewrite $ 16k^{2}-1 $ as:
$$ 16k^{2}-1 = (4k)^2 - (1)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 4k $ and $ II = 1 $ , we have:
$$ 16k^{2}-1 = (4k)^2 - (1)^2 = ( 4k-1 ) ( 4k+1 ) $$