When a square with side length $a$ units is divided into four regions as shown in the figure, region I represents a square with side length $b$ units.
For each $a$ and $b$ number satisfying this condition
$$a^{2} - 2ab + 2b^{2}$$
to which sum of areas of two regions is this expression equal?
A) I and II\\
B) I and IV\\
C) II and III\\
D) II and IV\\
E) III and IV