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Question:

Evaluate the following products without multiplying directly: (i) 103 × 107 (ii) 95 × 96 (iii) 104 × 96

Solution:

(i) 103 × 107 = (100 + 3)(100 + 7) = (100)² + (3 + 7)(100) + (3)(7) = 10000 + 1000 + 21 = 11021
(ii) 95 × 96 = (90 + 5)(90 + 6) = (90)² + (5 + 6)(90) + (5)(6) = 8100 + 990 + 30 = 9120
(iii) 104 × 96 = (100 + 4)(100 - 4) = (100)² - (4)² = 10000 - 16 = 9984