Mathematics Lab Activity-03 Class IX | Polynomials

   Lab Activity-03 Class iX

Mathematics Lab Activities on Polynomials for class IX students, with complete observation tables, strictly according to the CBSE syllabus.

Chapter - 02  polynomials

Activity - 03

Objective: 

To verify the algebraic identity : (a + b)² = a² + 2ab + b²

Material Required

Drawing sheet, cardboard, cello- tape, colored papers, cutter and ruler.

Procedure

1. Cut out a square of side length a units from a drawing sheet/cardboard and name it as square ABCD [see Fig. 1].

Figure 1

2. Cut out another square of length b units from a drawing sheet/cardboard and name it as square CHGF [see Fig. 2].

Figure 2

3. Cut out a rectangle of length a units and breadth b units from a drawing sheet/cardbaord and name it as a rectangle DCFE [see Fig. 3].

Figure 3

4. Cut out another rectangle of length b units and breadth a units from a drawing sheet/cardboard and name it as a rectangle BIHC [see Fig. 4].

Figure 4

5. Total area of these four cut-out figures
    = Area of square ABCD + Area of square CHGF + Area of rectangle DCFE + Area of rectangle BIHC

= a² + b² + ab + ba 

= a² + b² + 2ab.

6. Join the four quadrilaterals using cello-tape as shown in Fig. 5. Clearly, AIGE is a square of side (a + b). Therefore, its area is (a + b)². 

Figure 5

7. The  combined area of the constituent units = a² + b² + ab + ab = a² + b² + 2ab.

Hence, the algebraic identity (a + b)² = a² + 2ab + b²

Observations

On actual measurement:

a = 4 cm,    ⇒ a² = 16 cm² 

b = 2 cm,  ⇒ b² = 4 cm² 

2ab =  2 x 4 x 2  = 16 cm²

(a + b)   = 4 + 2  = 6 cm ,

Now

(a + b)² = (6)² = 36 cm²         

a² + b² + 2ab = 16 + 4 + 16 = 36 cm²     

Therefore, (a + b)² = a² + 2ab + b² .

Result : Identity  (a + b)² = a² + 2ab + b²   is verified.

Applications

 The identity may be used for

1. Calculating the square of a number expressed as the sum of two convenient numbers.

2. simplifications / factorisation of some algebraic expressions.

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