Q. 2 A4.1( 18 Votes )

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Answer :


(a – b)2 ≡ a2 - 2ab + b2


Consider a square with side a.i.e.a = 3


The square is divided into 4 regions.


It consists of 2 squares with sides a-b and b respectively and 2 rectangles with length and breadth as ‘a-b’ and ‘b’ respectively.


Here a = 3 and b = 1.Therefore the 2 squares consist of sides ‘3-1’ and ‘1’ respectively and 2 rectangles with length and breadth as ‘3-1’ and ‘1’ respectively.


Now area of figure I = Area of whole square with side ‘a’ i.e.3 units-Area of figure II


-Area of figure III –Area of figure IV


L.H.S of area of figure I = (3-1)(3-1) = 2(2) = 4 units


R.H.S = Area of whole square with side 3 units-Area of figure II with 1,(3-1)units


-Area of figure III with 1,(3-1) units –Area of figure IV with 1,1 unit = 32-(1×(3-1))-


(1×(3-1))-(1×1) = 4 units


L.H.S = R.H.S


Hence,the identity is verified.


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