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Math Help - Order of operations - parenthesis with 3 variables each

  1. #1
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    Order of operations - parenthesis with 3 variables each

    I am trying to brush up on my algebra. I am getting a different answer than the back of the book. The numbers are the same but the order is different.

    Write without parenthesis.

    (a + b + 2) (c + d -3)

    I get

    ac + ad -3a + bc +bd - 3d + 2c +2d - 6

    the back of the book shows

    ac + bc + ad + bd -3a - 3b + 2c + 2d - 6

    What is the correct order of distribution?
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  2. #2
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    I don't know that there is a "correct" order for such an exercise.

    And keep in mind that order doesn't matter for addition, so you only need to have the right terms; the order in which you list those terms shouldn't count against you, at least if you keep the constant terms at the end.
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  3. #3
    MHF Contributor alexmahone's Avatar
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    The book is right.

    (a+b+2)(c+d-3)
    = ac+bc+2c+ad+bd+2d-3a-3b-6
    = ac + bc + ad + bd -3a - 3b + 2c + 2d - 6
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  4. #4
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    Quote Originally Posted by mathmonkey View Post
    ...
    Write without parenthesis
    (a + b + 2) (c + d -3)

    I get

    ac + ad -3a + bc +bd - 3d + 2c +2d - 6

    the back of the book shows
    ...

    What is the correct order of distribution?
    Which ever is most meaningful to you.
    The procedure you use, is the one I find best.
    I proceed from left to right.
    After a is 'distributed', I strike it out.
    Then b and then 2.
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