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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

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12y ago

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Q: What is the geometrical proof of a-b whole square?
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