Polynomial identities

[SureHeIS]

 

[MathLover1]

c. (a - b) (a^2 - a b + b^2)
it should be (a + b) (a^2 - a b + b^2)

 

[nycmathguy]

c. (a - b) (a^2 - a b + b^2)
it should be (a + b) (a^2 - a b + b^2)

Why is C correct?

 

[MathLover1]

(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

 

[nycmathguy]

(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

This is not my thread. I still find it unbelievably disrespectful for SureHeIs to ignore your effort and hard work.

 

[nycmathguy]

View attachment 2917

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