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^2
C. a^3-b^3=(a-b)(a^2+ab+b^2)
D. a^2(b+c)=a^3(b/a+c)

Question

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^2
C. a^3-b^3=(a-b)(a^2+ab+b^2)
D. a^2(b+c)=a^3(b/a+c)

anonymous · Answer

$$\left(a^2+b^2\right) \left(c^2+d^2\right)=(a c-b d)^2+(a d+b c)\to $$$$a^2 c^2+a^2 d^2+b^2 c^2+b^2 d^2\neq a^2 c^2-2 a b c d+a d+b^2 d^2+b c  $$

anonymous · Answer

A.

alekos · Answer

by the same token for D

$$LHS \neq  RHS   $$

anonymous · Answer

It was D, thanks for the help anyways ^_^