CLASS : IX - MATHS : ACTIVITY RECORD

     ACTIVITY (4)

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

Materials Required:  Cardboard, glaze paper, scissor, sketch pen, transparent sheet, fevicol/gum.

Procedure:

(1) Take a cardboard base.

(2) Cut one square ABCD of side “a” units from a green glaze paper and paste it on the cardboard base. (Take a = 9 cm). (Fig (i))

(3) Cut one more square EFGD with side “b” units.(Take b = 3 cm) from a red glaze paper.

(4) Paste the smaller square EFGD on the bigger square ABCD as shown in figure (ii).

(5) Join F to B using sketch pen as shown in fig(ii).

(6) Cut out trapeziums congruent to GCBF and EFBA using transparent sheet and name them GCBF and EFBA respectively as shown in fig (iii).

(7) Arrange these trapeziums as shown in fig (iv).

Observation : From the figure, we observe that

Area of square ABCD – Area of square EFGD= Area of trapezium GCBF + Area of trapezium EFBA

= Area of rectangle GCEA = AE × EC

a² – b² =  ( a – b ) ( a + b )

Conclusion: We have verified the identity a² – b² =  ( a – b ) ( a + b ) .

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