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

In view of the graphic capabilities of this site, you will need to use a fair amount of imagination! Here goes: &lt;------a+b------&gt; &lt;----a----&gt;&lt;-b-&gt; +-----------+-----+ |. . . . . . . .|. . . .| |. . . P. . . .|. .Q. | |. . . . . . . .|. . . .| +-----------+-----+ |. . . R. . . .|. .S. | |. . . . . . . .|. . . .| +----------+-----+ Where P = a*a = a2 Q = a*b R = b*a = a*b S = b*b = b2 (a + b)2 = P + Q + R + S = a2 + ab + ab + b2 = a2 + 2ab + b2


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