Perfect Square Trinomials Worksheet
A Grade 9 math worksheet focusing on identifying, factoring, and expanding perfect square trinomials.
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Perfect Square Trinomials
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Read each question carefully and follow the instructions. Show all your work for full credit.
1. Which of the following is a perfect square trinomial?
x² + 6x + 5
x² - 8x + 16
x² + 4x + 3
x² - 10x + 20
2. What is the expanded form of (2x + 3)²?
4x² + 9
4x² + 6x + 9
4x² + 12x + 9
2x² + 12x + 9
3. A perfect square trinomial is a trinomial that results from squaring a .
4. The first and last terms of a perfect square trinomial are always squares.
5. Factor the following perfect square trinomial: x² + 10x + 25
6. Factor the following perfect square trinomial: 9y² - 24y + 16
7. The expression a² - 2ab + b² is always a perfect square trinomial.
True
False
8. To form a perfect square trinomial from x² + 14x + k, the value of k must be 49.
True
False
Match the trinomial with its factored form.
9. x² - 12x + 36
a. (x + 9)²
10. x² + 18x + 81
b. (x - 6)²
11. 4x² + 4x + 1
c. (2x + 1)²
12. Find the value of 'c' that makes the expression x² + 20x + c a perfect square trinomial.
13. The area of a square garden is represented by the expression 4x² - 28x + 49. What is the expression for the length of one side of the garden?