What is the formula of <math><msup><mfenced><mrow><mi>a</mi><mo>-</mo><mi>b</mi></mrow></mfenced><mn>3</mn></msup></math>?

Brandon White

Brandon White

Answered question

2022-11-24

What is the formula of ( a b ) 3 ?

Answer & Explanation

King Hansen

King Hansen

Beginner2022-11-25Added 6 answers

Find the formula for ( a b ) 3 .
The expression ( a b ) 3 can be written as follows:
( a b ) 3 = ( a b ) ( a b ) 2 . . . ( 1 )
Substitute the value ( a b ) 2 = a 2 + b 2 = 2 a b into (1):
( a b ) 3 = ( a b ) ( a 2 + b 2 2 a b )
Use the distributive property: a ( b + c ) = a b + a c :
( a b ) 3 = ( a 2 + b 2 2 a b ) b ( a 2 + b 2 2 a b )
( a b ) 3 = a 3 + a b 2 2 a 2 b b a 2 b 3 + 2 a b 2
( a b ) 3 = a 3 3 a 2 b b 3 + 3 a b 2
( a b ) 3 = a 3 b 3 3 a b ( a b )
Hence, the formula is ( a b ) 3 = a 3 b 3 3 a b ( a b )

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