Evaluate using the identity (a – b)² = a² – 2ab + b²

(i) (49)2 (ii) (9.8)2

(iii) (59)2 (iv) (198)2

The given identity is (a – b)² = a² – 2ab + b²

(i) (49)²

= (50 –1)²

Using the given identity

Here a = 50, b = 1

= 50² – 2× 50 × 1 +1²

= 2500 –100 +1

= 2401

(ii) (9.8)²

= (10 – 0.2)²

Using the given identity

Here a = 10, b = 0.2

= 10² – 2× 10 × 0.2 + (0.2)²

= 100 – 4 + 0.04

= 96.04

(iii) (59)2

= (60 – 1)²

Using the given identity

Here a = 60, b = 1

= 60² – 2× 60× 1 + 1²

= 3600 – 120 +1

= 3481

(iv) (198)2

= (200 –2)²

Using the given identity

Here a = 200, b = 2

= 200² – 2× 200 × 2 + 2²

= 40000 – 800 +4

= 39204