Factorize each of the following algebraic expression:

To factorise $\mathrm{a}^{2}+2 \mathrm{a}-3$, we will find two numbers $\mathrm{p}$ and $\mathrm{q}$ such that $\mathrm{p}+\mathrm{q}=2$ and $\mathrm{pq}=-3$.

Now,

$3+(-1)=2$

and

$3 \times(-1)=-3$

Splitting the middle term $2 \mathrm{a}$ in the given quadratic as $-\mathrm{a}+3 \mathrm{a}$, we get:

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

$=\left(a^{2}-a\right)+(3 a-3)$

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

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