Class 09 To verify the algebraic identity :(a+b)3 = a3 + b3 + 3a2b + 3ab2

 Activity 7

OBJECTIVE                

                                            

To verify the algebraic identity :(a+b)³ = a³ + b³ + 3a²b + 3ab²

 MATERIAL REQUIRED

Acrylic sheet, coloured papers, glazed papers, saw, sketch pen, adhesive, Cello-tape.

METHOD OF CONSTRUCTION

1.   Make a cube of side a units and one more cube of side b units (b < a), using acrylic sheet and cello-tape/adhesive [see Fig. 1 and Fig. 2].

 Similarly, make three cuboids of dimensions a×a×b and three cuboids of dimensions a×b×b [see Fig. 3 and Fig. 4].

3. Arrange the cubes and cuboids as shown in Fig. 5.

DEMONSTRATION

 Volume of the cube of side a = a×a×a = a³, volume of the cube of side b = b³ Volume of the cuboid of dimensions a×a×b = a²b, volume of three such cuboids

=   3a²b

 Volume of the cuboid of dimensions a×b×b = ab², volume of three such cuboids

=   3ab²

 Solid figure obtained in Fig. 5 is a cube of side (a + b)

 Its volume = (a + b)³

 Therefore, (a+b)³ = a³ + b³ + 3a²b + 3ab²

 Here, volume is in cubic units.

 OBSERVATION

 On actual measurement:

 a = ..............,         b = ............., a³  = ..............,

 So, a³ = ..............,       b³  = ............., a²b = ..............,            3a²b= ..............,

 ab² = ..............,   3ab² = ..............,          (a+b)³ = ..............,

 Therefore, (a+b)³ = a³ + b³ +3a²b + 3ab²

 APPLICATION

 The identity may be used for

 1.   calculating cube of a number expressed as the sum of two convenient numbers

 simplification and factorisation of algebraic expressions