Question

Verify the identity (a+b)2 = a + 2ab + b geometrically by taking
(1)
a=2 units, b=4 units
a=3 units , b= 1 unit

Answer 1

Given:

1) a=2 units, b=4 units

2) a=3 units , b= 1 unit

To Find :

Verify the identity (a + b)² ≡ a² + 2ab + b²

Solution:

1) a = 2 units, b = 4 units

(a + b)² ≡ a² + 2ab + b²

Substitute the values

(2+ 4)² ≡ 2² + 2(2)(4) + 4²

(6)² = 4 + 16 + 16

36 = 36

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2) a = 3 units, b = 1 unit

(a + b)² ≡ a² + 2ab + b²

Substitute the values

(3+ 1)² ≡ 3² + 2(3)(1) + 1²

(4)² = 9 + 6 + 1

16 = 16