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Focus E: Specialized Factoring Techniques

  1. x3 - 343 = (x)3 - (7)3                                          
                                = (x - 7)( x2 + 7x + (7)2)                     
                       = (x - 7)(x2 + 7x + 49)  

                            
  2. 27x3 - 1 = (3x)3 - (1)3  
                       = (3x - 1)[(3x)2 + (3x)(1) + (1)2]
                       = (3x - 1)(9x2 + 3x + 1)
  3. x3 - y3 = (x - y)(x2 + xy + y2)