Question

Verify the identity (a + b)² ≡ a² + 2ab + b² geometrically by taking a = 3 units, b = 1 unit

Answer 1

Area of a square AEGI = area of square ABCD + area of rectangle CDEF + area of square CFGH + area of rectangle BIHC. 

= 3 × 3 + 3 × 1 + 1 × 1+3 × 1 

= 9 + 3 + 1 + 3 

= 16 sq. units 

[∵ (3 + 1)² = 4² = 16]