Question

evaluate (998)^3 by using suitable identity

Answer 1

(998)^(3) to find it first we have to broke this into two simpler form

(1000-2)^(3) in this we have to use the equation (a-b)^(3)=(a)^(3)-b^(3)-3ab(a-b)

Now let's come to question (1000)^(3)-2^(3)-3×1000×2(1000-2)

1000000000-8-5988000

=994011992

Hence we got our answer

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Answer 2

Given,

• (998)³ is given.

To find,

• We have to evaluate (998)³ by using a suitable identity.

Solution,

We can simply evaluate (998)³ by using the following cubic identity:

       (a-b)³ = a³-b³-3ab(a-b)    (*)

We can write 998 as (1000-2), so we have to evaluate (1000-2)³ by using (*), we get

    (1000-2)³ = (1000)³-(2)³-3(1000)(2)(1000-2)

                 = 100000000-8-6000(1000-2)

                 = 100000000-8-6000000+12000

                 = 1000012000-6000008

                = 994011992

Hence, the evaluation of (998)³ by using a suitable identity is 994011992.