Q. 34.0( 4 Votes )

Evaluate:

(i) (95)3

(ii) (999)3

Answer :

(i) We know that,


(a – b)3 = a3 – b3 – 3ab (a – b)


Using this formula, we get


= (100 – 5)3


= (100)3 – (5)3 – 3 × 100 × 5 (100 – 5)


= 1000000 – 125 – (1500 × 95)


= 857375


(ii) We know that,


(a – b)3 = a3 – b3 – 3ab (a – b)


Using this formula, we get


= (1000 – 1)3


= (1000)3 – (1)3 – 3 × 1000 × 1 (1000 – 1)


= 1000000000 – 1 – 3000 (1000 – 1)


= 1000000000 – 1 – 3000 × 1000 +3000 ×1


= 997002999

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