Question

( 1 ) Evalute
(a) (99) 3
(b) (102) 3
(c) (998) 3​

Answer 1

Step-by-step explanation:

99×3=33. a is correct answer

Answer 2

answer

( a ) we write as 99 = 100 - 1

(99)3 =(100-1)3

using ( a - b )3 = a3 - b3 - 3ab ( a - b)

whear a = 100 & b = 1

= ( 100 )3 - ( 1 )3 ( 100 ) (1) ( 100 -1 )

= 10000000 - 1 - 300 (99)

= 1000000 - 1 - 29700

= 970299

( b ) we write 102 = 100 + 2

( 102 ) 3 = ( 100 + 2 )3

using ( a+ b)3 = a3 + b3 +3ab ( a+ b )

putting a = 100 & b = 2

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

= 1000000 + 8 + 600 (102)

= 1000000 + 8 + 61200

= 1061208

( c ) we write 998 = 1000- 2

(998)3 = ( 1000 - 2)3

using (a - b )3 = a3 - b3 - 3ab ( a - b )3

where as a = 1000& b=2

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

= 1000000000 - 8 - 6000 (998)

= 1000000000 - 5988008

= 994011992

hope it helps you