CBSE Class 9 Answered

   We  know that    ( X   +  Y )³     =  X³    + Y³  + 3XY ( X +Y)

                                  now  X ³ + Y ³      == ( X + Y )³ --- 3XY ( X+Y)

                                                                ( X +Y)   [  (X+Y)²   -- 3XY ]

                                                              ==  (X +Y) [ X^{2  +}  Y ²  +2XY  -3XY]

                                                             =   (X+Y)  [ X² +  Y²  - XY   ]  ==> (X+ Y)  { X²  -XY + Y^{2 ]}

 ^{similarly ,} X ³  -- Y ³   = (  X - Y )³   +  3 XY ( X- Y)

                                    = ( X--- Y )  [    (X -- Y )² + 3XY  ]

                                    == (X -Y)  [ X²   +Y² + XY ] ===> (X --Y)  [ X²  +  XY  +Y² ]