Which of the following is not a polynomial identity? A. (a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)B. (a+b)^2=a^2+2ab+b^2C. a^3-b^3=(a-b)(a^2+ab+b^2)D. a^2(b+c)=a^3(b/a+c),

Accepted Solution

Technically speaking, polynomial identities are true equations. So, in order to know which of the following is a polynomial identity, we need to solve each of them.

A. (a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)
     not a polynomial identity
B. (a+b)^2=a^2+2ab+b^2
     not a polynomial identity
C. a^3-b^3=(a-b)(a^2+ab+b^2)
     polynomial identity
D. a^2(b+c)=a^3(b/a+c)
     not a polynomial identity

Answer: C