prove the following

Asked by 100.akash | 30th Jul, 2008, 07:32: PM

Expert Answer:

   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) [ X2  +  Y +2XY  -3XY]

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

 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 ]

 

Answered by  | 31st Jul, 2008, 02:03: PM

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