Question

evaluate the following by using suitable identities
i) 998^3
ii) 12^3 - 8^3 - 5^3

Answer 1

i) 998 can be written as (1000 – 2)

∴ 998 = 1000 – 2

(998)^3 = (1000 – 2)^3

= (1000 – 2)3 = (1000)3 – (2)3 – 3 × 1000 × 2(1000 – 2) [(a – b)^3 = a^3 – b^3 – 3ab(a – b)]

= (998)^3 = 1000000000 − 8 – 5988000

∴ (998)^3  = 994011992

ii) Given, (12)³ + (-7)³ + (-5)³

We can see that a+b+c = 12-7-5 = 0

∴We can apply the identity a³ + b³ + c³ = 3abc

So, (12)³ + (-7)³ + (-5)³ = 3(12)(-7)(-5) = 1260

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