and 3 pairs of equal rectangles of dimensions corresponding to the side of each
square. Let the side of the squares thus formed be a, b and c respectively and so the
dimensions of the rectangles formed are a x b, b x c and c x a. Now observe that a
single square has been divided into 3 squares of different dimensions and 3 pairs of
equal rectangles. Thus the formation of the above said squares and rectangles reveal
that (A+B+C)^2 = A^2 + B^2 + C^2 +2AB +2BC + 2CA.
3.^12 +^41 +^18 +^161 +^321 +^641 +^1281 +^2561 +^5121 +^10241
Take a sheet of paper and fold it to form exactly two halves. Fold the one half again
to form another two halves. Similarly repeat the procedure, say for instance, ten
times so that the final folding gives a part which is 10241 of the original paper, thus
revealing the fact that^12 +^41 +^18 +^161 +^321 +^641 +^1281 +^2561 +^5121 +^10241
- Identity A^2 – B^2 = (A+B)(A-B) through dots
The identity can be illustrated through an example.
Let A = 5, B = 2
To prove, 5^2 – 2^2 = (5+2) (5-2)
Construct the following dots in a sheet of paper.
a
b
c
ab c
+ ... = 1
+ ... = 1
