Factorize each of the following quadratic polynomials by using the method of completing the square:

$a^{2}+2 a-3$

$=a^{2}+2 a+\left(\frac{2}{2}\right)^{2}-\left(\frac{2}{2}\right)^{2}-3 \quad\left[\right.$ Adding and subtracting $\left(\frac{2}{2}\right)^{2}$, that is, $\left.1^{2}\right]$

$=a^{2}+2 a+1^{2}-1^{2}-3$

$=(a+1)^{2}-4 \quad[$ Completing the square $]$

$=(a+1)^{2}-2^{2}$

$=[(a+1)-2][(a+1)+2]$

$=(a+1-2)(a+1+2)$

$=(a-1)(a+3)$