Page 30 - Mathematics Class - IX

ACTIVITY 2.5

OBJECTIVE
To verify the algebraic identity: a – b = (a – b) (a + ab + b )
3
2
2
3
MATERIALS REQUIRED
27 unit cubes made of wood (dimension is 1 unit × 1 unit × 1 unit)

PRE-REQUISITE KNOWLEDGE

1. Concept of volume of an object as the number of unit cubes in it.
2. Knowledge of the identity.
(a – b) (a + ab + b ) = (a – b) a + (a – b)(ab) + (a – b) b 2
2
2
2
THEORY
For the concepts of cube and cuboid refer to Activity 2.2.

PROCEDURE

For representing a – b :
3
3
1. Take a = 3 and make a cube of dimension 3 × 3 × 3 using 27 unit cubes Fig. (a).

Fig. (a)

2. Take b = 1 and remove a cube of dimension 1 × 1 × 1 from a (Figs. (b) and (c)).
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Fig. (b) Fig. (c)

3. Use the identity (a – b) (a + ab + b ) = (a – b) a + (a – b) (ab) + (a – b) b . For the given values of a
2
2
2
2
and b, the dimensions of cuboids formed in right hand side of the identity are as follows:
(a – b) a = 2 × 3 × 3 cubic units
2
(a – b) (ab) = 2 × 3 × 1 cubic units
(a – b) b = 2 × 1 × 1 cubic units
2
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