Polynomial identities

Discussion in 'Algebra' started by SureHeIS, May 2, 2022.

  1. SureHeIS

    SureHeIS

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    upload_2022-5-2_14-59-51.png
     
    SureHeIS, May 2, 2022
    #1
  2. SureHeIS

    MathLover1

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    c. (a - b) (a^2 - a b + b^2)
    it should be (a + b) (a^2 - a b + b^2)
     
    MathLover1, May 2, 2022
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    nycmathguy likes this.
  3. SureHeIS

    nycmathguy

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    Why is C correct?
     
    nycmathguy, May 18, 2022
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  4. SureHeIS

    MathLover1

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    (a - b) (a^2 - a b + b^2)...........exspand

    =a*a^2 - a*a b + a*b^2-b*a^2 -b*(- a b )-b* b^2
    =a^3 - a^2 b + a*b^2-b*a^2 + a b^2-b^3
    =a^3 - a^2 b + a*b^2-b*a^2 + a b^2-b^3.......cancel bolded and blue
    =a^3 -b^3

    since
    (a - b) (a^2 - a b + b^2)=a^3 -b^3, and c. a^3 +b^3=(a - b) (a^2 - a b + b^2) we see that c is not identity
     
    MathLover1, May 18, 2022
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    nycmathguy likes this.
  5. SureHeIS

    nycmathguy

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    This is not my thread. I still find it unbelievably disrespectful for SureHeIs to ignore your effort and hard work.
     
    nycmathguy, May 19, 2022
    #5
  6. SureHeIS

    nycmathguy

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    Don't forget to say THANK YOU to MathLover1 for answering YOUR thread.
     
    nycmathguy, May 19, 2022
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