Verifying Algebraic identity(I)

Today I will share with U how to verify cubic algebraic identities using unit cubes by activity method.

Proving the algebraic identity

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

Let a=3 and b=1.
To represent a^3 make a cube of dimension axaxa
i.e. 3x3x3 cubic units.

To represent 3a^2b make 3 cuboids of dimension
axaxb i.e. 3x3x1 cubic units.

To represent 3ab^2 make 3 cuboids of dimension
axbxb i.e. 3x1x1 cubic units.

To represent b^3 make a cube of dimension bxbxb
i.e. 1x1x1 cubic units.

Join all the cubes and cuboids formed in the previous
steps to make a cube of dimension (a+b) x (a+b) x (a+b)
i.e. 4x4x4 cubic units.

Observe the following:

The number of unit cubes in a^3 = ……..
The number of unit cubes in 3a^2b =………
The number of unit cubes in 3ab^2 =………
The number of unit cubes in b^3 =………
The number of unit cubes in a^3 + 3a^2b + 3ab^2 + b^3
= ……..
The number of unit cubes in (a+b)^3 =……

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 .

Students in my class find this activity ineresting and they enjoy playing with unit cubes and learning algebraic formulae by this method.

In my next post I will share the 2nd algebraic formula.

Bye..