Mathematics 21
5. Arrange these cut outs as shown in Fig. 5.
DEMONSTRATION
According to figure 1, 2, 3, and 4, Area of
square ABCD = a
2
, Area of square EBHI = b
2
Area of rectangle GDCJ = ab, Area of
rectangle IFJH = ab
From Fig. 5, area of square AGFE = AG × GF
= (a – b) (a – b) = (a – b)
2
Now, area of square AGFE = Area of square
ABCD + Area of square EBHI
– Area of rectangle IFJH – Area of rectangle
GDCJ
= a
2
+ b
2
– ab – ab
= a
2
– 2ab + b
2
Here, area is in square units.
OBSERVATION
On actual measurement:
a = .............., b = .............., (a – b) = ..............,
So, a
2
=
.............., b
2
= .............., (a – b)
2
= ..............,
ab = .............., 2ab = ..............
Therefore, (a – b)
2
= a
2
– 2ab + b
2
APPLICATION
The identity may be used for
1. calculating the square of a number expressed as a difference of two
convenient numbers.
2. simplifying/factorisation of some algebraic expressions.
Fig. 5