Polynomial identities

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

  1. SureHeIS

    SureHeIS

    Joined:
    Apr 21, 2022
    Messages:
    6
    Likes Received:
    0
    upload_2022-5-2_14-59-51.png
     
    SureHeIS, May 2, 2022
    #1
    1. Advertisements

  2. SureHeIS

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,292
    Likes Received:
    2,227
    c. (a - b) (a^2 - a b + b^2)
    it should be (a + b) (a^2 - a b + b^2)
     
    MathLover1, May 2, 2022
    #2
    nycmathguy likes this.
    1. Advertisements

  3. SureHeIS

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    4,164
    Likes Received:
    406
    Why is C correct?
     
    nycmathguy, May 18, 2022 at 8:38 AM
    #3
  4. SureHeIS

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,292
    Likes Received:
    2,227
    (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 at 3:30 PM
    #4
    nycmathguy likes this.
  5. SureHeIS

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    4,164
    Likes Received:
    406
    This is not my thread. I still find it unbelievably disrespectful for SureHeIs to ignore your effort and hard work.
     
    nycmathguy, May 19, 2022 at 12:18 AM
    #5
  6. SureHeIS

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    4,164
    Likes Received:
    406
    Don't forget to say THANK YOU to MathLover1 for answering YOUR thread.
     
    nycmathguy, May 19, 2022 at 12:20 AM
    #6
    1. Advertisements

Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.