Question

1-a cube -b cube-3ab
factorise

Answer 1

Identity / Property used :

x³ + y³ + z³ - 3xyz = ( x + y + z ) ( x² + y² + z² - xy - yz - zx )

Q : 1 - a³ - b³ - 3ab

We can also write this as :

( 1 )³ + ( - a )³ + ( - b )³ - 3 ( 1 ) ( a ) ( b )

Here, x = 1, y = - a, z = - b

= [ ( 1 ) + ( - a ) + ( - b ) ] [ ( 1 )² + ( - a )² + ( - b )² - ( 1 ) ( - a ) - ( - a ) ( - b ) - ( - b ) ( 1 ) ]

= ( 1 - a - b ) ( 1 + a² + b² + a - ab + b )