Question

Verify the identity (a + b)² ≡ a² + 2ab + b² geometrically by taking
(i) a = 2 units, b = 4 units
(ii) a = 3 units, b = 1 unit
(iii) a = 5 units, b = 2 unit

Answer 1

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

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3) a = 5 units, b = 2 unit

(a + b)² ≡ a² + 2ab + b²

Substitute the values

(5+ 2)² ≡ 5² + 2(5)(2) + 2²

(7)² = 25 + 20 + 4

49 = 49