Worksheet: Proving Polynomial Identities

In this worksheet, we will practice proving polynomial identities.

Q1:

Determine which of the following expressions is equivalent to ( 𝑥 + 𝑦 + 𝑧 ) .

  • A 2 𝑥 + 2 𝑦 + 2 𝑧 + 𝑥 𝑦 + 𝑥 𝑧 + 𝑦 𝑧
  • B 2 𝑥 + 2 𝑦 + 2 𝑧
  • C 𝑥 + 𝑦 + 𝑧
  • D 𝑥 + 𝑦 + 𝑧 + 𝑥 𝑦 + 𝑥 𝑧 + 𝑦 𝑧
  • E 𝑥 + 𝑦 + 𝑧 + 2 𝑥 𝑦 + 2 𝑥 𝑧 + 2 𝑦 𝑧

Q2:

Is the equation 𝑥 𝑦 = ( 𝑥 + 𝑦 ) ( 𝑥 𝑦 ) ( 𝑥 + 𝑦 ) an identity?

  • A yes
  • B no

Q3:

Is the equation 𝑥 𝑦 𝑥 𝑦 = 𝑥 + 𝑦 an identity?

  • A no
  • B yes

Q4:

Is the equation 𝑥 𝑦 = ( 𝑥 𝑦 ) 𝑥 + 𝑥 𝑦 + 𝑦 an identity?

  • A yes
  • B no

Q5:

Is the equation 𝑥 + 𝑦 𝑥 + 𝑦 = 𝑥 + 𝑦 an identity?

  • A No
  • B Yes

Q6:

Is the equation 𝑥 + 𝑦 𝑥 + 𝑦 = 𝑥 + 𝑦 an identity?

  • A Yes
  • B No

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.