A Visualization of A ^2 - B^2 =(A-B)(A+B)

^{A Visualization of A² - B^²
= (A-B)(A+B)}

Use a square (a 10x10 square is handy), to start. Call the side A, then the area is A².

The green length on top is B, and the area of the green square is B². The other length on top is A-B.

^{Cutting out B²leaves 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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