Grade 12 Polynomial Identities Worksheet
This worksheet focuses on polynomial identities, including sum/difference of cubes, perfect square trinomials, and difference of squares, suitable for Grade 12 math students.
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Grade 12 Polynomial Identities Worksheet
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Read each question carefully and use your knowledge of polynomial identities to solve them. Show all your work for full credit.
1. The difference of squares identity states that a² - b² = .
2. The sum of cubes identity is a³ + b³ = (a + b)( ).
3. A perfect square trinomial can be factored into the form (a + b)² or .
4. Which of the following is the correct expansion of (x - 3)²?
x² - 9
x² + 9
x² - 6x + 9
x² + 6x + 9
5. Factor the expression 4x² - 25y² using a polynomial identity.
(2x - 5y)(2x - 5y)
(2x - 5y)(2x + 5y)
(4x - 25y)(4x + 25y)
(4x + 5y)(4x - 5y)
6. Expand the expression (2a + 3b)³ using the binomial cube identity. Show all steps.
7. Factor the polynomial x³ - 8y³ completely.
8. The expression (a - b)² is equivalent to a² - b².
True
False
9. The identity (a + b)(a² - ab + b²) simplifies to a³ + b³.
True
False
Match each polynomial expression with its correct factored form.
10. x² - 100
a. (x + 5)²
11. x² + 10x + 25
b. (x - 10)(x + 10)
12. x³ - 27
c. (x - 3)(x² + 3x + 9)