Factorize each of the following algebraic expression:

To factorise $\mathrm{a}^{2}+14 \mathrm{a}+48$, we will find two numbers $\mathrm{p}$ and $\mathrm{q}$ such that $\mathrm{p}+\mathrm{q}=14$ and pq $=48$.

Now,

$8+6=14$

and

$8 \times 6=48$

Splitting the middle term 14a in the given quadratic as $8 a+6 a$, we get:

$\mathrm{a}^{2}+14 \mathrm{a}+48=\mathrm{a}^{2}+8 \mathrm{a}+6 \mathrm{a}+48$

$=\left(\mathrm{a}^{2}+8 \mathrm{a}\right)+(6 \mathrm{a}+48)$

$=\mathrm{a}(\mathrm{a}+8)+6(\mathrm{a}+8)$

$=(\mathrm{a}+6)(\mathrm{a}+8)$