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

 Activity 5

 OBJECTIVE                                                                    

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

METHOD OF CONSTRUCTION

 MATERIAL REQUIRED

Drawing sheets, cardboard, coloured papers, scissors, sketch pen, ruler, transparent sheet and adhesive.

1.   Take a cardboard of a convenient size and paste a coloured paper on it.

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

3.3.Cut out one square AEFG of side b units (b < a) from another drawing sheet [see Fig. 2].

4.   Arrange these squares as shown in Fig. 3.

 5.   Join F to C using sketch pen. Cut out trapeziums congruent to EBCF and GFCD using a transparent sheet and name them as EBCF and GFCD, respectively [see Fig. 4 and Fig. 5].

6. Arrange these trapeziums as shown in

Fig. 6.

 DEMONSTRATION

 Area of square ABCD = a²

 Area of square AEFG = b²

 In Fig. 3,

 Area of square ABCD – Area of square

 AEFG

 = Area of trapezium EBCF + Area of

 trapezium GFCD

 =  Area of rectangle EBGD [Fig. 6].

 =  ED×DG

 Thus, a² – b² = (a+b) (a–b)Fig. 6

Here, area is in square units.

OBSERVATION

On actual measurement:

 a = ..............,         b = .............., (a+b) = ..............,

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

 a2–b2 = .............., (a+b) (a–b) = ..............,

 Therefore, a²–b² = (a+b) (a–b)

 APPLICATION

 The identity may be used for

 1.   difference of two squares

 2.   some products involving two numbers

 3.   simplification and factorisation of algebraic expressions.