Verify the all algebraic identity (a+b)^2 = a^2 + 2ab + b^2 by an activity method.
Answers
Answer:
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Step-by-step explanation:
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).
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)
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.
Learning Outcome
The identity (a+b)2 = a2 + 2ab + b2 is verified by cutting and pasting of paper. This identity can be verified geometrically by taking other values of a and b.
