Class 09 To verify the algebraic identity :(a – b)2 = a2 – 2ab + b2

 

Activity 4 

OBJECTIVE                                                                    

To verify the algebraic identity :(a – b)² = a² – 2ab + b²

 MATERIAL REQUIRED

Drawing sheets, cardboard, coloured papers, scissors, ruler and adhesive.

METHOD OF CONSTRUCTION

1.    Cut out a square ABCD of side a units from a drawing sheet/cardboard [see Fig. 1].

 2.   Cut out a square EBHI of side b units (b < a) from a drawing sheet/cardboard [see Fig. 2].

 3.   Cut out a rectangle GDCJ of length a units and breadth b units from a drawing sheet/cardboard [see Fig. 3].

 4.   Cut out a rectangle IFJH of length a units and breadth b units from a drawing sheet/cardboard [see Fig. 4].

5. Arrange these cut outs as shown in Fig. 5.

 DEMONSTRATION

 According to figure 1, 2, 3, and 4, Area of square ABCD = a², Area of square EBHI = b²

 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		Fig. 5
GDCJ
= a2	+ b2 – ab – ab
= a2	– 2ab + b2

 Here, area is in square units.

 OBSERVATION

 On actual measurement: 

a = ..............	,	b = ..............		, (a – b) = ..............	,
So, a2 = ..............	,	b2 =	..............	, (a – b)2 = ..............	,
ab = ..............	,	2ab	= ..............

 Therefore, (a – b)² = a² – 2ab + b²

 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.