Using identities, evaluate (i) 71², (ii) 99², (iii) 102², (iv) 998², (v) 5.2², (vi) 297 × 303, (vii) 78 × 82, (viii) 8.9², (ix) 1.05 × 9.5

i) 71² = (70 + 1)² = (70)² + 1² + 2(70)(1) ∵ [(a + b)² = a² + b² + 2ab] = 4900 + 1 + 140 = 5041
ii) 99² = (100 - 1)² = (100)² + 1² - 2(100)(1) ∵ [(a - b)² = a² + b² - 2ab] = 10000 + 1 - 200 = 9801
iii) 102² = (100 + 2)² = (100)² + 2² + 2(100)(2) ∵ [(a + b)² = a² + b² + 2ab] = 10000 + 4 + 400 = 10404
iv) 998² = (1000 - 2)² = (1000)² + 2² - 2(1000)(2) ∵ [(a - b)² = a² + b² - 2ab] = 1000000 + 4 - 4000 = 996004
v) 5.2² = (5 + 0.2)² = (5)² + (0.2)² + 2(5)(0.2) ∵ [(a + b)² = a² + b² + 2ab] = 25 + 0.04 + 2 = 27.04
vi) 297 × 303 = (300 - 3)(300 + 3) = (300)² - (3)² ∵ [(a² - b²) = (a + b)(a - b)] = 90000 - 9 = 89991
vii) 78 × 82 = (80 - 2)(80 + 2) = (80)² - (2)² ∵ [(a² - b²) = (a + b)(a - b)] = 6400 - 4 = 6396
viii) (8.9)² = (9 - 0.1)² = (9)² + (0.1)² - 2(9)(0.1) ∵ [(a - b)² = a² + b² - 2ab] = 81 + 0.01 - 1.8 = 79.21
ix) 1.05 × 9.5 = 105/100 × 95/10 = 10000/1000 × (105 × 95) = 10000/1000 × (100 + 5)(100 - 5) = 10/1000 × [(100)² - (5)²] = 10/1000 × (10000 - 25) = 10/1000 × 9975 = 9975/100 = 99.75