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Math Help - Polynomial question

  1. #1
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    Polynomial question

    According to Edward T. Dowling within Schaum's Outline of Theory and problem of Mathematical methods for business and economics:

     (3x^3 - 5x^2 y^2 - 2y^3)(7x-4y) = 21x^2 - 12x^y - 35x^3y^2 +20x^2y^3 - 14xy^3 + 8y^4

    Can you clarify?
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  2. #2
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    Re: Polynomial question

    Try using "tex" inside your brackets instead of "math."
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  3. #3
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    Re: Polynomial question

    Quote Originally Posted by jon80 View Post
    According to Edward T. Dowling within Schaum's Outline of Theory and problem of Mathematical methods for business and economics:

     (3x^3 - 5x^2 y^2 - 2y^3)(7x-4y) = 21x^2 - 12x^y - 35x^3y^2 +20x^2y^3 - 14xy^3 + 8y^4

    Can you clarify?
     (3x^3 - 5x^2 y^2 - 2y^3)(7x-4y) = 21x^2 - 12x^y - 35x^3y^2 +20x^2y^3 - 14xy^3 + 8y^4

    It should be : 21x^4 instead of 21x^2

    And it should be: -12x^3y instead of -12x^y

    The rest is correct
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  4. #4
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    Re: Polynomial question

    Quote Originally Posted by psolaki View Post
     (3x^3 - 5x^2 y^2 - 2y^3)(7x-4y) = 21x^2 - 12x^y - 35x^3y^2 +20x^2y^3 - 14xy^3 + 8y^4

    It should be : 21x^4 instead of 21x^2

    And it should be: -12x^3y instead of -12x^y

    The rest is correct
    Thanks, could you show me the pattern of simplification, because when I was multiplying factor by factor the factors of my result were not adding up correctly, so I thought I might be mistaken in my approach.
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  5. #5
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    Re: Polynomial question

    Quote Originally Posted by jon80 View Post
    Thanks, could you show me the pattern of simplification, because when I was multiplying factor by factor the factors of my result were not adding up correctly, so I thought I might be mistaken in my approach.
    What did you get when you tried? Did you follow the approach I suggested on the previous thread?
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  6. #6
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    Re: Polynomial question

    I did not quite understand the method of working it out by looking at your answer, sorry, would you clarify?
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  7. #7
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    Re: Polynomial question

    Quote Originally Posted by jon80 View Post
    I did not quite understand the method of working it out by looking at your answer, sorry, would you clarify?
    You have (3x^3- 5x^2y^2- 2y^3)(7x- 4y)
    By the "distributive law" this is the same as
    (3x^3- 5x^2y^2- 2y^2)(7x)+ (3x^3- 5x^2y^2- 2y^3)(-4y)
    Usin the distributive law again,
    (3x^3)(7x)+ (-5x^2y^2)(7x)+ (-2y^2)(7x)+ (3x^3)(-4y)+ (-5x^2y^2)(-4y)+ (-2y^3)(-4y)
    = (21x^(3+1)- 35x^{2+1}y^2- 14xy^2)+ (-12x^3y+ 20x^2y^{2+1}+ 8y^{3+1}
    = (21x^4- 35x^3y^2- 14xy^2)+ (-12x^3y+ 20x^2y^3+ 8y^4)
    = 21x^4- 35x^3y^2- 12x^3y+ 20x^2y^3+ 8y^4
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