# Polynomial identities

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

1. ### SureHeIS

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SureHeIS, May 2, 2022

2. ### 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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3. ### nycmathguy

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Why is C correct?

nycmathguy, May 18, 2022 at 8:38 AM
4. ### 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 at 3:30 PM
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5. ### 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 at 12:18 AM
6. ### nycmathguy

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Don't forget to say THANK YOU to MathLover1 for answering YOUR thread.

nycmathguy, May 19, 2022 at 12:20 AM

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