Question

Verify the identity(a + b)(a – b) = a² – b² geometrically by taking a = 2 units, b = 1 unit

Answer 1

a² – b² = Area of Fig I. + Area of Fig II

= a(a – b) + b(a – b)

= (a + b) (a – b)

= (2 + 1)(2 – 1)

= 3 × 1 = 3

a² – b² = 3 sq. units

[∵ (2² – 1²) = 4 – 1 = 3]