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A^2  - b^2                SEE the enclosed picture

draw a square of side  a (from point O to A).  So let square be OAPQ. 
Let us say b is less than a. Mark B which is b distance from O on the line OA.
Now draw a square of side b, with OB being one side of it.  Call it OBCD.
So the area between the two squares will be a^2 - b^2. Shade that area by crossed lines. 

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