2021/036) Simplify : $\sqrt{4 -4a + a^2} + \sqrt{4 + 4a + a^2}$, if $a < -2 $

We have $\sqrt{4 -4a + a^2} = \sqrt{(a-2)^2}= | a- 2 | $

as $a < -2 $ so  $\sqrt{4 -4a + a^2} = 2 - a$

Further we have $\sqrt{4 + 4a + a^2} = \sqrt{(a+2)^2}= | a + 2 | $

as $a < -2 $ so  $\sqrt{4 -4a + a^2} = - 2 - a$

adding we get $\sqrt{4 -4a + a^2}  +  \sqrt{4 + 4a + a^2}= - 2a$