Verify the identity (a – b)² ≡ a² - 2ab + b²geometrically by taking

a = 5 units, b = 2 units

(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.