Question

Verify the algebraic identity (a+b+c)2 =a2+b2+c2+2ab+2bc+2ca by cutting And pasting method

Answer 1

Answer:

objective

To verify the identity (a + b)2 = a2 + 2ab + b2 by paper cutting and pasting.

Prerequisite Knowledge

Area of a square = (side)2.

Area of a rectangle = l x b.

Materials Required

A sheet of white paper, three sheets of glazed paper (different colours), a pair of scissors, gluestick and a geometry box.

Procedure

Take distinct values of a and b, say a = 4 units, b = 2 units

Cut a square of side a (say 4 units) on a glazed paper (blue).

Cut a square of side b (say 2 units) on glazed paper (pink).

Now, cut two rectangles of length a (4 units) and breadth b (2 units) from third glazed paper (red).

cbse-class-9-maths-lab-manual-algebraic-identity-a-b2-a2-2ab-b2-1

Draw a square PQRS of (a+ b) = (4 + 2), 6 units on white paper sheet as shown in fig. (i).

Paste the squares I and II and two rectangles III and IV on the same white squared paper. Arrange all the pieces on the white square sheet in such a way that they form a square ABCD fig. (ii)

cbse-class-9-maths-lab-manual-algebraic-identity-a-b2-a2-2ab-b2-2

cbse-class-9-maths-lab-manual-algebraic-identity-a-b2-a2-2ab-b2-3

Observation

Area of the square PQRS on the white sheet paper.

(a+b)2 = (4+2)2 = 6 x 6 = 36 sq. units ……….(i)

Area of two coloured squares I and II

area of Ist square = a2 = 42 = 16 sq.units

area of IInd square = b2 = 22 = 4 sq.units

Area of two coloured rectangles III and IV = 2(a x b) = 2(4 x 2) = 16 sq. units

Now, total area of four quadrilaterals (calculated)

= a2 + b2 + 2(ab)

= 16+4+16

= 36 sq. units ……….(ii)

Area of square ABCD = Total area of four quadrilaterals = 36 sq. units

Equating (i) and (ii)

Area of square PQRS = Area of square ABCD

i.e., (a+b)2 = a2 + b2 + 2ab

Result

Algebraic identity (a+b)2 = a2 + 2ab + b2 is verified

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