Multiply or divide as indicated. a 3 − 8 b 3 a 2 − 2 a b − 15 b 2 ⋅ a 2 + 4 a n − 45 b 2 a 2 + 7 a b − 18 b 2

Question

Multiply or divide as indicated.                    a        3            −      8              b        3                            a        2            −      2      a      b      −      15              b        2              ⋅                    a        2            +      4      a      n      −      45              b        2                            a        2            +      7      a      b      −      18              b        2

Mackenzie Lutz · Accepted Answer

a        3            −      8              b        3                            a        2            −      2      a      b      −      15              b        2              ⋅                    a        2            +      4      a      n      −      45              b        2                            a        2            +      7      a      b      −      18              b        2            Let us simplify inequality      a    2    +  4  a  b  −  45      b    2      =      a    2    +  9  a  b  −  5  a  b  −  45      b    2      =  a  (  a  +  9  b  )  −  5  b  (  a  +  9  b  )    =  (  a  +  9  b  )  (  a  −  5  b  )So,      a    2    +  4  a  b  −  45      b    2      =  (  a  +  9  b  )  (  a  −  5  b  )        a    2    −  2  a  b  −  15      b    2      =      a    2    −  5  a  b  +  3  a  b  −  15      b    2      =  a  (  (  a  −  5  b  )  +  3  b  (  a  −  5  b  )    =  (  a  −  5  b  )  (  a  +  3  b  )So,       a    2    −  2  a  b  −  15      b    2      =  (  a  −  5  b  )  (  a  +  3  b  )        a    2    +  7  a  b  −  18      b    2      =      a    2    +  9  a  b  −  2  a  b  −  18      b    2      =  a  (  a  +  9  b  )  −  2  b  (  a  +  9  b  )    =  (  a  +  9  b  )  (  a  −  2  b  )So,      a    2    +  7  a  b  −  18      b    2      =  (  a  +  9  b  )  (  a  −  2  b  )Now                    a        3            −      8              b        3                            a        2            −      2      a      b      −      15              b        2              ⋅                    a        2            +      4      a      b      −      45              b        2                            a        2            +      7      a      b      −      18              b        2                =                    a        3            −      8              b        3                    (      a      −      5      b      )      (      a      +      3      b      )        ⋅            (      a      +      9      b      )      (      a      −      5      b      )              (      a      +      9      b      )      (      a      −      2      b      )      Then,  =                    a        3            −      (      2      b              )        3                    (      a      +      3      b      )      (      a      −      2      b      )          =            (      a      −      2      b      )      (              a        2            +      2      a      b      +      (      2      b              )        2            )              (      a      +      3      b      )      (      a      −      2      b      )          =                    a        2            +      2      a      b      +      4              b        2                    a      +      3      b

Multiply or divide as indicated. (a^3-8b^3)/(a^2-2ab-15b^2)*(a^2+4ab-45b^2)/(a^2+7ab-18b^2)

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