= ( x + y ) m − k ?Is it always true that: ( x + y ) m ( x + y ) k where m , k ∈ N ?I tried it with a few numbers and it seems to work every time.

Question

=            (      x      +      y      )              m      −      k       ?Is it always true that:                     (        x        +        y        )                    m                            (        x        +        y        )                    k             where    m  ,  k  ∈      N  ?I tried it with a few numbers and it seems to work every time.

Semaj Stark · Accepted Answer

It should be                                                        x              +              y                                      m                                                          x              +              y                                      k                                                          =                              (            x            +            y                          )                              1                m                                                          (            x            +            y                          )                              1                k                                                                                      =        (        x        +        y                  )                                                    1                m                            −                              1                k                                                                                      =        (        x        +        y                  )                                                                      k                  −                  m                                                  k                  m                                                                                                      =                              (            x            +            y                          )                                                k                  −                  m                                                                          k            m

= <mroot> ( x + y ) </mrow> <mstyle mathsize="1.2em"

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