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Math Help - simplifying long algebraic expressions

  1. #1
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    simplifying long algebraic expressions

    Hi,

    I have an expression that I need to simplify:

    (i - n)(i - m)(i - y)(i - s)

    I know how to simplify this algebraically using the FOIL method. I did it and I have the answer, but I'm really hoping there might be a different way to do it. Is there an easier way to simplify long algebraic expressions like this, especially given that i is a factor in each part?
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  2. #2
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    Quote Originally Posted by absvalue View Post
    Hi,

    I have an expression that I need to simplify:

    (i - n)(i - m)(i - y)(i - s)

    I know how to simplify this algebraically using the FOIL method. I did it and I have the answer, but I'm really hoping there might be a different way to do it. Is there an easier way to simplify long algebraic expressions like this, especially given that i is a factor in each part?
    Is this i the imaginary unit? Or just a regular variable?

    Keep in mind i is NOT a factor in each term.

    i(1-n)\neq(i-n) We can't start pulling out i's.
    Last edited by Kasper; September 1st 2009 at 01:59 PM.
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  3. #3
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    I can't believe that I've been staring at the problem for 2 hours and missed that. Thanks for your help! I'll be sure to remember that.
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  4. #4
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    Wait... quick question.

    i(1 - n)(1 - m)(1 - y)(1 - s)

    Wouldn't this evaluate to be:

    <br />
(i - ni)(i - mi)(i - yi)(i - si)

    And wouldn't that have a different value than the original expression? Please correct me if I'm missing something. Thanks.
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  5. #5
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    Kasper has changed his/her post.
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  6. #6
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    If the i you are dealing with IS the imaginary unit, expand and you will end up with a i^4 and a i^2 term, which you can use to simplify into whole numbers.
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  7. #7
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    Quote Originally Posted by Kasper View Post
    Is this i the imaginary unit? Or just a regular variable?

    Keep in mind i is NOT a factor in each term.

    i(1-n)\neq(i-n) We can't start pulling out i's.
    Sorry, I didn't see that you had updated your post. i is just a regular variable.
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  8. #8
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    Quote Originally Posted by absvalue View Post
    Sorry, I didn't see that you had updated your post. i is just a regular variable.
    I'm not sure then, are you sure the question was to simplify or to expand? This expression is in its simplest form.
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  9. #9
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    Quote Originally Posted by Kasper View Post
    This expression is in its simplest form.
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  10. #10
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    Quote Originally Posted by Kasper View Post
    I'm not sure then, are you sure the question was to simplify or to expand? This expression is in its simplest form.
    Yes, just double checked. The question was to simplify.
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  11. #11
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    Quote Originally Posted by absvalue View Post
    Wait... quick question.

    i(1 - n)(1 - m)(1 - y)(1 - s)

    Wouldn't this evaluate to be:

    <br />
(i - ni)(i - mi)(i - yi)(i - si)
    No, it wouldn't. Since you have only one i, it can be multiplied into only one term you could write it as
    (i-ni)(1- m)(1- y)(1- x) or
    (1- n)(i- mi)(1- y)(1- x) or
    (1- n)(1- m)(i- yi)(1- x) or
    (1- n)(1- m)(1- y)(i- xi).

    And wouldn't that have a different value than the original expression? Please correct me if I'm missing something. Thanks.
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