Question

To evaluate (99)3 , best option is expansion of (a) (95 + 4)3 (b) (90 + 9)3 (c) (100 - 1)3 (d) (98 + 1)3

Answer 1

Answer:

To evaluate (99)³, the best option is expansion of (100-1)³

Answer 2

Given :

4 options are given.

(a) (95 + 4)³

(b) (90 + 9)³

(c) (100 - 1)³

(d) (98 + 1)³

To find:

Best option out of four to evaluate (99)³

solution :

To evaluate (99)³

number 99 is closest to 100 , it will be easy to do calculations with number 100 and 1.

The formula used will be

(a - b ) ³= a³ - b³ - 3ab ( a -b )

( 99) = (100 ) ³- (1) ³- (3 x 100 x 1) ( 100 - 1)

= 1000000 - 1 - (300 ) (99)

= 999,999 - 29700

= 970299

Hence best option to evaluate (99)³ is expansion of (100-1)³ so option (c) is the correct option.