1 . (993)³
2 . (1002)³
Evaluate the following products using "ALGEBRAIC IDENTITIES"
Answers
Answer:
write both of these in the form of (a +- b) ^3
Step-by-step explanation:
1) (1000-7)^3
2) (1000+2)^3
Answer:
1. 979146657
2. 1006012008
Step-by-step explanation:
1.
( 993 )³
( 993 )³= ( 1000 - 7 )³
( 993 )³
= ( 1000 - 7 )³
( a - b )³ = a³ - b³ - 3ab ( a - b ) { Identify }
where,
a = 1000
b = 7
= 1000³ - 7³ - 3 ( 1000 ) ( 7 ) [ 1000 - 7 ]
= 1000000000 - 343 - 21000 [ 1000 - 7 ]
= 1000000000 - 343 - 21000000 + 147000
= 1000000000 + 147000 - 343 - 21000000
= 1000147000 - 21000343
= 979146657
Therefore, ( 993 )³ = 979146657
2.
( 1002 )³
= ( 1000 + 2 )³
( a + b )³ = a³ + b³ + 3ab ( a + b ) { Identify }
where,
a = 1000
b = 2
= 1000³ + 2³ + 3 ( 1000 ) ( 2 ) [ 1000 + 2 ]
= 1000000000 + 8 + 6000 [ 1000 + 2 ]
= 1000000000 + 8 + 6000000 + 12000
= 1006012008
Therefore, ( 1002 )³ = 1006012008