How do I get from 1 3 n ( n + 1 ) ( n + 2 ) + ( n + 2 ) ( n + 1 ) to ( 1 3 n + 1 ) ( n + 1 ) ( n + 2 )?

Question

How do I get from       1    3    n  (  n  +  1  )  (  n  +  2  )  +  (  n  +  2  )  (  n  +  1  ) to       (          1      3        n    +    1    )    (  n  +  1  )  (  n  +  2  )?

Jaelyn Levine · Accepted Answer

Just factor out   (  n  +  1  )  (  n  +  2  ).      1    3    n      (    n    +    1    )    (    n    +    2    )    +      (    n    +    1    )    (    n    +    2    )    =      (          1      3        n    +    1    )        (    n    +    1    )    (    n    +    2    )  Also notice that in your working, you have involved       n    4  , which should not happen since we are only working with addition of polynomials of degree at most 3.

kjukks1234531 · Accepted Answer

Your mistake is here   →      1    3    n  (  n  +  1  )  (  n  +  2  )  +  (  n  +  2  )  (  n  +  1  )  =      (          1      3              n      2        +          1      3        n    )                                            (                          1              3                                      n              2                        +                          2              3                        n            )                          ⏟                            should stay         (        n        +        2        )              +  (  n  +  2  )  (  n  +  1  )You have done the following   a  b  c  =  (  a  b  )  (  a  c  ) instead of   a  b  c  =  (  a  b  )  c

How do I get from 13/n(n+1)(n+2)+(n+2)(n+1) to (13/n + 1)(n+1)(n+2)?

Answered question

Answer & Explanation

New Questions in Pre-Algebra