Question

solve e part .factorize

Answer 1

Heya User,

--> x³ - 12x( x - 4 ) - 64    

--> x³ - 3(x)(4)( x - 4 ) - ( 4 )³        ----> [ i ]

---> We know :-> ( a - b )³ = [ a³ - 3ab ( a - b ) - b³ ]

Comparing with the above [ i ] -->

--> [ x³ - 3(x)(4)( x - 4 ) - ( 4 )³ ] = [ x - 4 ]³  

^_^ Done ..

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--> x³ - 12x( x - 4 ) - 64    

= x³ - 64 - 12x( x - 4 )
= ( x - 4 )( x² + 4x + 16 ) - 12x( x - 4 )

= ( x - 4 )( x² + 4x - 12x + 16 )
= ( x - 4 )( x² - 4x - 4x + 16 )
= ( x - 4 )( x( x - 4 ) - 4( x - 4 ) )
= ( x - 4 )( x - 4 )²

= ( x - 4 )³  √√√            <---- And We're done ^_^ 

Answer 2

Hey!

x^3-12x(x-4)-64

Splitting 12x,
We get, 3(x)(4)

x^3-3(x)(4)(x-4)-64 [Equation (a)]


According to the identity,
(a-b)^3={a^3-b^3-3ab(a-b)}

Thus, using Equation (a) in the identity,

[x^3-(4)^3-3(x)(4)(x-4)]
= (x-4)^3


Hope it helps...!!! ^_^