Polynomial Identities Worksheet
Explore and apply common polynomial identities such as difference of squares, sum/difference of cubes, and perfect square trinomials.
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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. Which of the following is the correct expansion of (a + b)²?
a² + b²
a² - b²
a² + 2ab + b²
a² - 2ab + b²
2. The identity a³ - b³ is equivalent to:
(a - b)(a² + ab + b²)
(a - b)(a² - ab + b²)
(a + b)(a² - ab + b²)
(a + b)(a² + ab + b²)
3. The difference of squares identity states that a² - b² = .
4. A perfect square trinomial can be factored into the form (ax ± b)², where the middle term is the product of 'ax' and 'b'.
5. Expand the expression (3x + 2y)² using a polynomial identity.
6. Factor the expression 49m² - 64n² completely.
Match each polynomial expression with its equivalent identity.
7. (x - y)(x² + xy + y²)
a. x² - y²
8. (x + y)(x - y)
b. x³ - y³
9. (x + y)(x² - xy + y²)
c. x³ + y³
10. (a - b)² = a² - b²
True
False
11. The expression x² + 10x + 25 is a perfect square trinomial.
True
False
12. Use polynomial identities to simplify the expression (x + 3)(x - 3) + (x + 2)².