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Question:

Using a² - b² = (a+b)(a-b), find (i) 51² - 49² (ii) 1.02² - 0.98² (iii) 153² - 147² (iv) 12.1² - 7.9²

Solution:

i) 51² - 49² = (51 - 49)(51 + 49) = 2 × 100 = 200
ii) (1.02)² - (0.98)² = (1.02 - 0.98)(1.02 + 0.98) = 0.04 × 2 = 0.08
iii) 153² - 147² = (153 - 147)(153 + 147) = 6 × 300 = 1800
iv) 12.1² - 7.9² = (12.1 - 7.9)(12.1 + 7.9) = 4.2 × 20 = 84