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A Visualization of A2 - B2
= (A-B)(A+B)
}
Use a square (a 10x10 square is handy), to start.
Call the side A, then the area is A^{2 }.

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The green length on top is B, and the area of the green square is B^{2}.
The other length on top is A-B.

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Cutting out B2 leaves A2 -
B2.
Cut off the shaded piece above, rotate it, and
put it at the bottom, as below
What's on the left is a rectangle, the width is A-B and the length is A+B
and the area is still A2 - B2 ;
another name for its area is (A-B) (A+B). So A2
- B2 = (A-B) (A+B).
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}