Answer :
(a – b)2 ≡ a2 - 2ab + b2
Consider a square with side a.i.e.a = 5
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 = 5 and b = 2.Therefore the 2 squares consist of sides ‘5-2’ and ‘2’ respectively and 2 rectangles with length and breadth as ‘5-2’ and ‘2’ respectively.
Now area of figure I = Area of whole square with side ‘a’ i.e.5 units-Area of figure II
-Area of figure III –Area of figure IV
L.H.S of area of figure I = (5-2)(5-2) = 3(3) = 9 units
R.H.S = Area of whole square with side 5 units-Area of figure II with 2,(5-2)units
-Area of figure III with 2,(5-2) units –Area of figure IV with 2,2 units = 25-(2×3)-
( 2×3)-22 = 25-6-6-4 = 9 units
L.H.S = R.H.S
Hence,the identity is verified.
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