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

Answer 1

In view of the graphic capabilities of this site, you will need to use a fair amount of imagination! Here goes:

<------a+b------>

<----a----><-b->

+-----------+-----+

|. . . . . . . .|. . . .|

|. . . 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