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We will use paper cutting to prove the algebraic formula
Difference of 2 squares a and b, a square - b square = (a+b) (a-b)
We will first take a square and lets say its side is a.
So its area is a times a or a square.
Now lets make another square of side b in one corner.
The area of this smaller square is b times b or b square.
Now we will cut this smaller square from the larger.
The remaining paper should be a square - b square.
We will now show that this paper left is a rectangle of size a+b and a-b.
Fr this cut along the small rectangular piece as shown and place it at the bottom as shown.
You will now have a rectangle of size a+b as width and height as a-b.
So the difference of two squares is a square - b square = (a+b) (a-b) This work was supported by IUCAA and Tata Trust.
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