Question

evaluate the following using suitable identities : a) (99)cube b) (102) cube c) (998)cube

Answer 1

It is known that,
(a+b)3=a3+b3+3ab(a+b)and(a−b)3=a3−b3−3ab(a−b)

(i) (99)3 = (100 − 1)3
= (100)3 − (1)3 − 3(100) (1) (100 − 1)
= 1000000 − 1 − 300(99)
= 1000000 − 1 − 29700
= 970299

(ii) (102)3 = (100 + 2)3
= (100)3 + (2)3 + 3(100) (2) (100 + 2)
= 1000000 + 8 + 600 (102)
= 1000000 + 8 + 61200
= 1061208

(iii) (998)3= (1000 − 2)3
= (1000)3 − (2)3 − 3(1000) (2) (1000 − 2)
= 1000000000 − 8 − 6000(998)
= 1000000000 − 8 − 5988000
= 1000000000 − 5988008
= 994011992

Answer 2

Answer:

Step-by-step explanation:

    (99)3 = (100 − 1)3

= (100)3 − (1)3 − 3(100) (1) (100 − 1)

= 1000000 − 1 − 300(99)

=                 1000000 − 1 − 29700

= 970299

(102)3 = (100 + 2)3

= (100)3 + (2)3 + 3(100) (2) (100 + 2)

= 1000000 + 8 + 600 (102)

= 1000000 + 8 + 61200

= 1061208

(998)3=        (1000 − 2)3

= (1000)3 −         (2)3 − 3(1000) (2) (1000 − 2)

=           1000000000 − 8 − 6000(998)

=         1000000000 − 8 − 5988000

=            1000000000 − 5988008

=        994011992

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