Question

which of the following expressions are perfect-square trinomials? check all of the boxes that apply.

(x^2 - 16x - 64)
(4x^2 + 12x + 9)
(x^2 + 20x + 100)
(x^2 + 4x + 16)

Explanation:

Step1: Define perfect-square trinomial form

$$(ax + b)^2 = a^2x^2 + 2abx + b^2$$

Step2: Test the first expression

$$x^2 - 16x - 64 eq (x - 8)^2 = x^2 - 16x + 64$$

Step3: Test the second expression

$$4x^2 + 12x + 9 = (2x + 3)^2$$

Step4: Test the third expression

$$x^2 + 20x + 100 = (x + 10)^2$$

Step5: Test the fourth expression

$$x^2 + 4x + 16 eq (x + 4)^2 = x^2 + 8x + 16$$

Answer:

• \(4x^2 + 12x + 9\)
• \(x^2 + 20x + 100\)