Factorize each of the following algebraic expression:

$(x+2)^{2}-6(x+2)+9$

$=(\mathrm{x}+2)^{2}-2 \times(\mathrm{x}+2) \times 3+3^{2}$

$=[(\mathrm{x}+2)-3]^{2}$

$=(\mathrm{x}+2-3)^{2}$

$=(\mathrm{x}-1)^{2}$

$=(\mathrm{x}-1)(\mathrm{x}-1)$