Activity(3)
Aim: Using the unit cubes verify the algebraic identity
(a-b)^3 = a^3 -3a^2b+3ab^2- b^3.
Material required: Unit cubes
Procedure:
1) Let a=3 and b=1.
(a-b)^3 = (2) ^3
To represent (a-b) ^3 make a cube of dimension (a-b) x (a-b) x (a-b) i.e. 2x2x2 cubic units

2) To represent (a) ^3 make a cube of dimension 3x3x3 cubic units



3) To represent 3ab^2 make 3 cuboids of dimension 3x1x1 cubic units.

4) To represent a^3 + 3ab^2, join the cube and the cuboids formed in steps 2 and 3.

5) To represent a^3 + 3ab^2- 3a^2b extract from the shape formed in the previous step 3 cuboids of dimension 3x3x1.

6) To represent a^3 + 3ab^2- 3a^2b-b^3 extract from the shape formed in the previous step 1 cube of dimension 1x1x1.



7) Arrange the unit cubes left to make a cube of dimension2x2x2 cubic units.

Observation:
The number of unit cubes in a^3 = …27…..
The number of unit cubes in 3ab^2 =…9……
The number of unit cubes in 3a^2b=…27…
The number of unit cubes in b^3 =…1…
The number of unit cubes in a^3 - 3a^2b + 3ab^2- b^3 =..8..
The number of unit cubes in (a-b) ^3 =…8...
The number of unit cubes in (a-b) ^3 = number of unit cubes

in a^3 -3a^2b+3ab^2-b^3.

Result:
(a-b)^3 = a^3 -3a^2b+3ab^2- b^3.

ACTIVITY(2)
(Activity 2)
Aim: - To verify the algebraic identity
(a+b)^3=a^3+3a^2b+3ab^2+b^3 using unit cubes.
Material required: - Unit Cubes
Procedure:-
Step1:-Let a=2 units and b=1unit.
Therefore, (a+b) = 3 units(a+b)^3 = 3^3=3 x3x3 cubic units.Make a cube of dimension 3x3x3 cubic units.

Step2:-a=2 unitsTherefore, a^3 =2^3=2x2x2 cubic unitsMake a cube of dimension 2 x2x2 .It represents a^3

Step3:- b=1 unitTherefore, b^3 =1^3=1x1x1 cubic units.

Step4:-3a^2b =3(2x2x1)Make 3 cuboids of this dimension .These 3 pieces will represent 3a^2b.

Step5:-3ab^2 = 3(2x1x1)
Make 3 cuboids of this dimension .These 3 pieces will represent 3ab^2.

Observation: -
1)The number of unit cubes in (a+b) ^3 =…27…
2)The number of unit cubes in a^3 = …8…..
3)The number of unit cubes in 3a^2b =…12……
4)The number of unit cubes in 3ab^2 =……6…
5)The number of unit cubes in b^3 =……1…
6)The number of unit cubes in a^3 + 3a^2b + 3ab^2 + b^3= …27…..

Result:- (a+b)^3=a^3+3a^2b+3ab^2+b^3

ACTIVITY(1)

Activity(1)
Aim: Making square root spiral