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