Aim: Using
the unit cubes verify the algebraic identity
Material required: Unit cubes
Procedure:
Take any suitable value for a and b.
Let a=3 and b=1.
1) 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 a x a x a i.e. 3x3x3 cubic units .
3) To represent 3ab2 make 3 cuboids of dimension a x b x b i.e. 3x1x1 cubic units .
4) To represent a3 + 3ab2 , join the cube and the cuboids formed in steps 2 and 3 .
5) To represent a3 + 3ab2- 3a2b extract from the shape formed in the previous step 3 cuboids of dimension 3x3x1.
6) To represent a3 + 3ab2- 3a2b-b3 extract from the shape formed in the previous step 1 cube of dimension 1 x 1 x 1.
7) Arrange the unit cubes left to make a cube of dimension2x2x2 cubic units.
Calulations:
1)The number of unit cubes in a3 = ……..
2)The number of unit cubes in 3ab2 =………
3)The number of unit cubes in 3a2b=………
4)The number of unit cubes in b3 =………
5)The number of unit cubes in a3 - 3a2b + 3ab2- b3 = ……..
6)The number of unit cubes in (a-b)3 =…...
Observation: It is observed that the number of unit cubes in (a-b)3 is equal to the number of unit cubes in a3 - 3a2b + 3ab2- b3.
Write the result: …………………………………………
Repeat the activity by taking different values of a and b.
