Which of the following is factorised form of ${\mathrm{a}}^2+4\mathrm{a}+4$?

The given expression is  ${\mathrm{a}}^2+4\mathrm{a}+4$ . 

It can be factorised using the identity, ${(\mathrm{a}+\mathrm{b})}^2=({\mathrm{a}}^2+2\mathrm{ab}+{\mathrm{b}}^2)$

So, ${\mathrm{a}}^2+4\mathrm{a}+4$ can be written as:

${\mathrm{a}}^2+4\mathrm{a}+4={\mathrm{a}}^2+2(\mathrm{a}\times 2)+4$           

                          $={(\mathrm{a}+2)}^2$

Hence, the factorised form of ${\mathrm{a}}^2+4\mathrm{a}+4$ is ${(\mathrm{a}+2)}^2$.