$a^2-b^2 \,=\, (a+b)(a-b)$
The $a^2-b^2$ identity represents the difference of two square quantities and it can be written in factoring form as the product of binomials $a+b$ and $a-b$. The factoring form of $a^2-b^2$ formula can be derived in mathematics geometrically on the basis of areas of geometric shapes.
The width of the upper rectangle is $a-b$ and the length of the lower rectangle is also $a-b$ geometrically. If the lower rectangle is rotated by $90^\circ$, then the widths of both rectangles become same and it is useful to join them together as a rectangle.
In first step, it is derived that the area of subtracted shape is $a^2-b^2$ and the same shape is now transformed as a rectangle, whose area is ${(a+b)}{(a-b)}$.
Therefore, the areas of both shapes should be equal geometrically.
$\,\,\, \therefore \,\,\,\,\,\, a^2-b^2 \,=\, (a+b)(a-b)$
Geometrically, it is proved that the $a^2$ subtracted $b^2$ is equal to the product of the binomials $a+b$ and $a-b$.
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