Given the graphic capability of this site, you are going to have
to use some imagination!
<---------a--------->
<---a-b---><--b-->
+-----------+-------+
|...............|..........|
|.......P......|....Q...|
|...............|..........|
+-----------+-------+
|.......R......|....S....|
|...............|..........|
+-----------+-------+
In the above graphic, P, S and the whole figure are meant to be
squares.
The total area is P+Q+R+S = a2
P = (a-b)2
Q = b*(a-b) = (a-b)*b = a*b - b2
R = (a-b)*b = a*b = a*b - b2
and
S = b2
Now, P = {P+Q+R+S} - Q - R - S
= a2 - ab + b2 - ab + b2 - b2
= a2 - 2ab + b2