Evaluate :
(i) 993
(ii) 1013
(iii) 983
(iv) (102)3
(v) (1002)3
(i) (100 – 1)3
Here the identity used is
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(100 – 1)3
= (100)3 + 3(100)2 (– 1) + 3(100) (– 1)2 + (– 1)3
= 1000000 – 30000 + 300 – 1
= 970299
(ii) 1013
Here the identity used is
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(101)3 = (100 + 1)3
= 1003 + 3 × 1002 × 1 + 3 × 100 × 12 + 13
= 1000000 + 30000 + 300 + 1
= 1030301
(iii) 983
= (100 – 2)3
Here the identity used is
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(100 – 2)3
= 1003 + (– 2)3 + 3(100)2(– 2) + 3(100)(– 2)2
= 1000000 – 8 – 60000 + 1200
= 941192
(iv) (102)3
Here the identity used is
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(100 + 2)3
= 1003 + 3(100)2 (2) + 3(2)2(100) + (2)3
= 1000000 + 60000 + 1200 + 8
= 1061208
(vi) (1002)3
= (1000 + 2)3
Here the identity used is
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(1000 + 2)3
= 10003 + 3 × 10002(2) + 3 × 1000 × (2)2 + 23
= 1000000000 + 6000000 + 12000 + 8
= 1006012008
Couldn't generate an explanation.
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