Polynomial Identities Worksheet
Grade 11 math worksheet covering polynomial identities, including factoring sums/differences of cubes and squares, and binomial expansions.
Includes
Standards
Topics
Polynomial Identities
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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?
x² - 9
x² + 9
x² - 6x + 9
x² - 3x + 9
2. Which expression represents the factorization of 8x³ + 27?
(2x + 3)(4x² - 6x + 9)
(2x + 3)(4x² + 6x + 9)
(2x - 3)(4x² + 6x + 9)
(2x - 3)(4x² - 6x + 9)
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.
True
False
2. (x + y)⁴ = x⁴ + y⁴ is a polynomial identity.
True
False
Match the polynomial expression with its correct factored or expanded form.
1. x² - 49
a. (x - 5)(x² + 5x + 25)
2. x³ - 125
b. (x + 7)(x - 7)
3. (x + 2)³
c. x³ + 6x² + 12x + 8