Polynomial Identities Worksheet

Polynomial Identities

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. The sum of cubes identity is a³ + b³ =  .

2. The difference of cubes identity is a³ - b³ =  .

3. The difference of squares identity is a² - b² =  .

4. The square of a binomial (a + b)² =  .

1. Which of the following is equivalent to (x - 3)²?

2. Which expression represents the factorization of 8x³ + 27?

1. Factor the expression completely: 16x⁴ - 81y⁴

2. Expand the expression: (2x + 5)³

3. Prove the identity: (a + b)(a² - ab + b²) = a³ + b³

1. The identity (a - b)(a² + ab + b²) = a³ - b³ is always true.

2. (x + y)⁴ = x⁴ + y⁴ is a polynomial identity.

Match the polynomial expression with its correct factored or expanded form.