By using suitable identities, evaluate the following:
(99)3
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(99)3 = (100 - 1)3
Using (a - b)3 = a3 - b3 - 3(a)(b)(a - b),
(100 - 1)3 = (100)3 - (1)3 - 3(100)(1)(100 - 1)
= 1000000 - 1 - 300(99)
= 1000000 - 1 - 29700
= 970299
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Use (a - b)2 = a2 - 2ab + b2 to evaluate the following:
(9.8)2
(103)3
(10.1)3
If 2a - b + c = 0, prove 4a2 - b2 + c2 + 4ac = 0