Polynomial Identities Worksheet
This worksheet focuses on polynomial identities, including perfect square trinomials, difference of squares, and sum/difference of cubes for Grade 9 Math students.
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 identity for the square of a binomial is (a + b)² = .
2. The difference of squares identity is a² - b² = .
3. The sum of cubes identity is a³ + b³ = .
4. Which of the following is the correct expansion of (x - 3)²?
x² - 9
x² + 9
x² - 6x + 9
x² + 6x + 9
5. Which identity is most appropriate to factor 4y² - 25?
Perfect square trinomial
Difference of cubes
Sum of cubes
Difference of squares
6. Expand the expression (2x + 5)². Show your work.
7. Factor the expression 9a² - 49b². Show your work.
8. The expression (a - b)³ expands to a³ - 3a²b + 3ab² - b³.
True
False
9. The identity a³ - b³ can be factored as (a - b)(a² - ab + b²).
True
False
Match the polynomial identity with its correct factored/expanded form.
10. (x + y)²
a. (a - b)(a² + ab + b²)
11. x² - y²
b. x² + 2xy + y²
12. a³ - b³
c. (x - y)(x + y)
13. Prove the identity (a + b)³ = a³ + 3a²b + 3ab² + b³ by expanding the left side.