Question

Evaluate the following using suitable identities: (i) (99)³ (ii) (102)³ (iii) (998)³

Answer 1

It is known that, 

(a + b)³ = a³ + b³ + 3ab(a + b) 

nd (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

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(ii) (102)³ = (100 + 2)³ 

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

= 1000000 + 8 + 600 (102) 

= 1000000 + 8 + 61200 

= 1061208

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(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.