Verify the identity (a + b) (a – b) ≡ a² – b² geometrically by taking

a = 3 units, b = 2 units

Remove square from this whose side is ‘b’.(b<a)

Consider a square with side ‘a’.

We get the above figure by removing the square with side ‘b’.It consists of 2 parts

I and II.

So a²-b² = Area of figure I + Area of figure II = a(a-b) + b(a-b) = (a-b)(a + b)

Thus a²-b² = (a-b)(a + b).

Here a = 3 units and b = 2 units

So,L.H.S = a²-b² = 3²-2² = 5 units

R.H.S = (a-b)(a + b) = (3-2)(3 + 2) = 1(5) = 5 units

Therefore L.H.S = R.H.S

Hence,the identity is verified.