By using suitable identities, evaluate the following:
(103)3
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(103)3 = (100 + 3)3
Using (a + b)3 = a3 + b3 + 3(a)(b)(a + b),
(100 + 3)3 = (100)3 + (3)3 + 3(100)(3)(100 + 3)
= 1000000 + 27 + 900(103)
= 1000000 + 27 + 92700
= 1092727
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Use (a - b)2 = a2 - 2ab + b2 to evaluate the following:
(997)2
(9.8)2
(99)3
(10.1)3