ACTIVITY 2 : To verify algebraic identity
(a + b )2 = a 2 + b2+ 2ab by paper cutting and pasting method.
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Answers
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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
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