Sunday, July 16, 2023

Class 09 To verify the algebraic identity :(a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

 

Activity 6 







OBJECTIVE

MATERIAL REQUIRED

 

To verify the algebraic identity :

Hardboard, adhesive, coloured

 

(a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

papers, white paper.

 

 

 

METHOD OF CONSTRUCTION

 

 

 1.   Take a hardboard of a convenient size and paste a white paper on it.

 2.   Cut out a square of side a units from a coloured paper [see Fig. 1].

 3.   Cut out a square of side b units from a coloured paper [see Fig. 2].

 4.   Cut out a square of side c units from a coloured paper [see Fig. 3].

 5.   Cut out two rectangles of dimensions a× b, two rectangles of dimensions b × c and two rectangles of dimensions c × a square units from a coloured paper [see Fig. 4].

6.   Arrange the squares and rectangles on the hardboard as shown in Fig. 5.

DEMONSTRATION

From the arrangement of squares and

 rectangles in Fig. 5, a square ABCD is

 obtained whose side is (a+b+c) units.

 Area of square ABCD = (a+b+c)2 . 

Therefore, (a+b+c)2  = sum of all the

 

squares and rectangles shown in Fig. 1 to

 

Fig. 4.

Fig. 5

 =   a2 + ab + ac + ab + b2 + bc + ac + bc + c2

 =  a2 + b2 + c2 + 2ab + 2bc + 2ca

 Here, area is in square units.

 OBSERVATION

 On actual measurement:

a = ..............

,

b = ..............

, c = ..............

,

 

 

So, a2 = ..............

,

b2 = ..............

, c2= ..............

, ab=

..............

,

bc= ..............

,

ca = ..............

,2ab = ..............

,

2bc =

..............,

2ca= ..............

,

a+b+c = ..............

,

(a+b+c)2 =

..............

,

 Therefore, (a+b+c)2 = a2 + b2 +c2 +2ab + 2bc + 2ca

 APPLICATION

 The identity may be used for

 1.   simiplification/factorisation of algebraic expressions

 calculating the square of a number expressed as a sum of three convenient numbers.

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