Question

find the cube of 102 using (a+b)³=a³-3a²b+3ab²-b³​

Answer 1

Answer:

102 = 100+2

(a+b)³=a³+3a²b+3ab²+b³

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

= 1000000+60000+1200+8

= 1061208

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Answer 2

(102 )³ can be written as (100 + 2)³

(102 )³ can be written as (100 + 2)³Using identity here ;

(102 )³ can be written as (100 + 2)³Using identity here ;( a + b )³ = a³ + b³ + 3ab ( a + b )

(102 )³ can be written as (100 + 2)³Using identity here ;( a + b )³ = a³ + b³ + 3ab ( a + b )⇒ (100 + 2)³

(102 )³ can be written as (100 + 2)³Using identity here ;( a + b )³ = a³ + b³ + 3ab ( a + b )⇒ (100 + 2)³⇒ (100)³ + (2)³ + 3 × 100 × 2 (100 + 2)

(102 )³ can be written as (100 + 2)³Using identity here ;( a + b )³ = a³ + b³ + 3ab ( a + b )⇒ (100 + 2)³⇒ (100)³ + (2)³ + 3 × 100 × 2 (100 + 2)⇒ 1000000 + 8 + 600 ( 102 )

(102 )³ can be written as (100 + 2)³Using identity here ;( a + b )³ = a³ + b³ + 3ab ( a + b )⇒ (100 + 2)³⇒ (100)³ + (2)³ + 3 × 100 × 2 (100 + 2)⇒ 1000000 + 8 + 600 ( 102 )⇒ 1000000 + 8 + 61200

(102 )³ can be written as (100 + 2)³Using identity here ;( a + b )³ = a³ + b³ + 3ab ( a + b )⇒ (100 + 2)³⇒ (100)³ + (2)³ + 3 × 100 × 2 (100 + 2)⇒ 1000000 + 8 + 600 ( 102 )⇒ 1000000 + 8 + 61200⇒ 1061208

(102 )³ can be written as (100 + 2)³Using identity here ;( a + b )³ = a³ + b³ + 3ab ( a + b )⇒ (100 + 2)³⇒ (100)³ + (2)³ + 3 × 100 × 2 (100 + 2)⇒ 1000000 + 8 + 600 ( 102 )⇒ 1000000 + 8 + 61200⇒ 1061208Therefore the answer is 1061208.