Simplifying 3 ( a 1 / 4 + 4 ) 2 a − 32 a 1 / 2 I have a fraction 3 a 1 / 4 + 12 2 a − 32 a 1 / 2 which I have factored out into 3 ( a 1 4 + 4 ) 2 a − 32 a 1 2 but checking out W|A I also get that there ought to be also 3 2 ( a 1 / 4 − 4 ) a 1 / 2 I can't figure out what steps should I take between what I've got and that simpler form though.

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Simplifying             3      (              a                  1                      /                    4                    +      4      )              2      a      −      32              a                  1                      /                    2                    I have a fraction             3              a                  1                      /                    4                    +      12              2      a      −      32              a                  1                      /                    2                     which I have factored out into             3              (                  a                                    1              4                                      +        4        )                    2      a      −      32              a                              1            2                               but checking out W|A I also get that there ought to be also       3          2      (              a                  1                      /                    4                    −      4      )              a                  1                      /                    2                    I can&#039;t figure out what steps should I take between what I&#039;ve got and that simpler form though.

enfujahl · Accepted Answer

2  a  −  32      a          1              /            2        =  2      (    a    −    16          a              1                  /                2              )    =  2      a          1              /            2            (          a              1                  /                2              −    16    )  Since this is of the form       a    2    −      b    2   we can factor as follows  2      a          1              /            2            (          a              1                  /                2              −    16    )    =  2      a          1              /            2            (          a              1                  /                4              −    4    )        (          a              1                  /                4              +    4    )  I think that is enough to get through this.

Jayla Christensen · Accepted Answer

Note that                    2        a        −        32                  a                                    1              2                                                          =        2                  a                                    1              2                                      (                  a                                    1              2                                      −        16        )                                          =        2                  a                                    1              2                                                (                                    (                              a                                                      1                    4                                                              )                        2                    −                      4            2                    )                                                  =        2                  a                                    1              2                                                (                      a                                          1                4                                              −          4          )                          (                      a                                          1                4                                              +          4          )                .

Simplifying 3 ( a <mrow class="MJX-TeXAtom-ORD">

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