Today I am sharing with U the 2nd cubic algebraic activity which can be done

using the unit cubes.

•To prove the algebraic identity

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

using unit cubes.

Take any suitable value for a and b.

Let a=3 and b=1.

To represent (a-b)^3 make a cube of dimension

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

using unit cubes.

Take any suitable value for a and b.

Let a=3 and b=1.

To represent (a-b)^3 make a cube of dimension

(a-b) x (a-b) x (a-b) i.e. 2x2x2 cubic units as shown below.

To represent (a)^3 make a cube of dimension a x a x a

i.e. 3x3x3 cubic units as shown below.

To represent 3ab^2 make 3 cuboids of dimension

To represent (a)^3 make a cube of dimension a x a x a

i.e. 3x3x3 cubic units as shown below.

To represent 3ab^2 make 3 cuboids of dimension

a x b x b i.e. 3x1x1 cubic units as shown below.

To represent a^3 + 3ab^2 , join the cube and the cuboids

To represent a^3 + 3ab^2 , join the cube and the cuboids

formed in the previous step 3 cuboids of dimension

3x3x1 to get the shape shown below.

To represent a^3 + 3ab^2- 3a^2b-b^3 extract from the

shape formed in the previous step 1 cube of dimension

Arrange the unit cubes left to make a cube of dimension

2x2x2 cubic units.

Observe the following

•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…

It is observed that the number of unit cubes

in (a-b)^3 is equal to the number of unit cubes

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

2x2x2 cubic units.

Observe the following

•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…

It is observed that the number of unit cubes

in (a-b)^3 is equal to the number of unit cubes

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

Using the same strategy we can verify the other cubic identities.

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