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Find the squares of the following numbers using the identity (a - b)2 = a2 - 2ab + b2 :(i) 395 (ii) 995 (iii)495 (iv) 498 (v) 99 (vi) 999 (vii)599 |
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Answer» (i) 395 395 = (400 – 5)2 = (400)2 + 52 – 2 (400) (5) = 160000 + 25 – 4000 = 156025 (ii) 995 995 = (1000 – 5)2 = (1000)2 + 52 – 2 (1000) (5) = 1000000 + 25 – 10000 = 990025 (iii)495 495 = (500 – 5)2 = (500)2 + 52 – 2 (500) (5) = 250000 + 25 – 5000 = 245025 (iv) 498 498 = (500 – 2)2 = (500)2 + 22 – 2 (500) (2) = 250000 + 4 – 2000 = 248004 (v) 99 99 = (100 – 1)2 = (100)2 + 12 – 2 (100) (1) = 10000 + 1 – 200 = 9799 (vi) 999 999 = (1000 – 1)2 = (1000)2 + 12 – 2 (1000) (1) = 1000000 + 1 – 2000 = 998001 (vii)599 (600 – 1)2 = (600)2 + 12 – 2 (600) (1) = 360000 + 1 – 1200 = 358801 |
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