Factorize each of the following algebraic expression:

$x^{2}+2 x+1-9 y^{2}$

$=\left(x^{2}+2 x+1\right)-9 y^{2}$

$=\left(x^{2}+2 \times x \times 1+1\right)-9 y^{2}$

$=(x+1)^{2}-(3 y)^{2}$

$=[(x+1)-3 y][(x+1)+3 y]$

$=(x+1-3 y)(x+1+3 y)$

$=(x+3 y+1)(x-3 y+1)$