x3 + 8y3 + 64z3 - 24xyzfactorize
Answer :
We have : x3 + 8y3 + 64z3 - 24 xyz , So
x3 + ( 2y )3 + ( 4z )3 - 3( x ) ( 2y ) ( 4 z )
And we know
a3 + b3 + c3 - 3abc = ( a + b + c ) ( a2 + b2 + c2 - ab - bc - ca ) , So
x3 + ( 2y )3 + ( 4z )3 - 3( x ) ( 2y ) ( 4 z ) = ( x + 2y + 4z ) [ x2 + ( 2y ) 2 + ( 4z )2 - ( x )( 2y ) - ( 2y )( 4z ) - ( 4z ) ( x ) ]
= ( x + 2y + 4z ) [ x2 + 4y 2 + 16 z 2 - 2x y - 8yz- 4 x z ] ( Ans )
We have : x3 + 8y3 + 64z3 - 24 xyz , So
x3 + ( 2y )3 + ( 4z )3 - 3( x ) ( 2y ) ( 4 z )
And we know
a3 + b3 + c3 - 3abc = ( a + b + c ) ( a2 + b2 + c2 - ab - bc - ca ) , So
x3 + ( 2y )3 + ( 4z )3 - 3( x ) ( 2y ) ( 4 z ) = ( x + 2y + 4z ) [ x2 + ( 2y ) 2 + ( 4z )2 - ( x )( 2y ) - ( 2y )( 4z ) - ( 4z ) ( x ) ]
= ( x + 2y + 4z ) [ x2 + 4y 2 + 16 z 2 - 2x y - 8yz- 4 x z ] ( Ans )