Question

8xcube+27ycube+zcube_18×y​

Answer 1

8x³ + 27y³ + z³ - 18xy

Sol :

( 2 x )³ + ( 3 y )³ + ( z )³ - 3 ( 2 x ) ( 3 y ) ( z ).

Using identity ,

a³ + b³ + c³ - 3 abc = ( a + b + c ) ( a² + b² + c² - ab - bc - ca )

Now,

( 2 x + 3 y + z ) { ( 2 x )² + ( 3 y )² + ( z )² - ( 2 x ) ( 3 y ) - ( 3 y ) z - z ( 2 x ) }

= ( 2 x + 3 y + z ) ( 4 x² + 9 y² + z² - 6 xy - 3 yz - 2 xz )