Mathematics Lab Activity-04 Class IX | Polynomials

    Lab Activity-04 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 - 04

Objective: 

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

Material Required

Drawing sheets, cardboard, coloured papers, scissors, ruler and adhesive.

Procedure

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].

Figure 1

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

Figure 2

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

Figure 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].

Figure 4

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

Figure 5

6. From the arrangement of squares and rectangles in Fig. 5, a square ABCD is obtained whose side is (a + b + c) units.
7. 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.
        = a² + ab + ac + ab + b² + bc + ac + bc + c²
        = a² + b² + c² + 2ab + 2bc + 2ca

Observations

On actual measurement:

a = 4, b = 2, c = 1,

So, a² = 16,    b² = 4,    c² = 1, 

ab = 8,     bc = 2,     ca = 4,

2ab = 16,     2bc = 4,     2ca = 8, 

a + b + c = 7,     (a + b + c)² = 49,

a² + b² + c² + 2ab + 2bc + 2ca = 16 + 4 + 1 + 16 + 4 + 8 = 49

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

Result : Identity  (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.   is verified.

Applications

 The identity may be used for

1. Simplification / factorisation of algebraic expressions

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

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