MATH SOLVE

7 months ago

Q:
# 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

Answer: C

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

Answer: C