Final Cover - For Printing

IDENTITIES

1. (A+B)^2 = A^2 + 2AB + B^2

Take a square sheet of paper. Fold it either vertically or horizontally so that the paper

is divided into two parts one larger and the other smaller. Bring the vertex of the

smaller part to coincide with the impression already created and mark the point where

the vertex and the impression of the folding coincide. Fold the paper across that

point to form a perpendicular line with the former. Now the paper is divided into four

parts viz., two squares and two rectangles. Name the side of the two squares as ‘a’

and ‘b’. Consequently the dimensions of the two equal rectangles will be a x b. Here

the square with side (a+b), and hence the area (a+b)^2 is now divided into four parts,

two squares with the area a^2 and b^2 respectively and two rectangles with area ‘ab’

each. This implies that (a+b)^2 = a^2 + 2ab+b^2.

2. (A+B+C)^2 = A^2 + B^2 + C^2 +2AB +2BC + 2CA

Cut a sheet of paper in the form of a square. Fold the paper say vertically to some

suitable measurement. Now fold the paper horizontally so as to form two squares-one

small and one big and two equal rectangles. Repeat the procedure again to divide the

bigger square into two resulting in the formation of three squares of different sides

Module 90 : Identities

a

b

ab