Question

(998)³,Evaluate it using suitable identites.

Answer 1

Solution :

Q. (998)³ = (1000 - 2)³

Using identity: (a - b)³ = a³ - b³ - 3ab (a-b)

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

= 1000000000 - 8 - 6000(998)

= 1000000000 - 8 - 5988000

= 1000000000 - 5988008

= 994011992

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Answer 2

Solution :

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We know the algebraic identity :

( a - b )³ = a³ - 3a²b + 3ab² - b³

Or

( a - b )³ = a³ - b³ - 3ab( a - b )

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Now ,

( 998 )³

= ( 1000 - 2 )³

= (1000)³ - 2³ - 3×1000×2(1000-2)

= 1000000000-8-6000×998

= 1000000000 - 8 - 5988008

= 994011992

Therefore ,

998³ = 994011992

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