Evaluate each of the following:
(i) (103)³
(ii) (98)³
(iii) (9.9)³
(iv) (10.4)³
(v) (598)³
(vi) (99)³
Answers
(i) Given : (103)³ = (100 + 3)³
Using identity,
(a + b)³ = a³ + b³ + 3ab(a + b)
(100 + 3)³ = (100)³ + 3³ + (3 × 100 × 3)(100 + 3)
= 1000000 + 27 + 900(100 + 3)
= 1000000 + 27 + 90000 + 2700
(103)³= 1092727
(v) Given :(598)³
Using identity,
(a – b)³ = a³–b³ – 3ab(a – b)
(600 – 2)³ = (600)³ - 2³ - (3 × 600 × 2)(600 – 2)
= 216000000 – 8 – 3600(600 – 2)
= 216000000 – 8 - 2160000 + 7200
(598)³= 213847192
(vi) Given : (99)³ = (100 - 1)³
Using identity,
(a – b)³ = a³ – b³ – 3ab(a – b)
(100 – 1)³ = (100)³ – 1³– (3 × 100 × 1)(100 – 1)
= 1000000 - 1 - 300(100 - 1)
= 1000000 - 1 - 30000 + 300
(99)³= 970299
SOLUTION (ii) , (iii) and (iv) is in the attachment below.
HOPE THIS ANSWER WILL HELP YOU…..
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