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

$x^2 - 16x - 64$

$4x^2 + 12x + 9$

$x^2 + 20x + 100$

$x^2 + 4x + 16$

Question

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

$x^2 - 16x - 64$

$4x^2 + 12x + 9$

$x^2 + 20x + 100$

$x^2 + 4x + 16$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Perfect-Square Trinomials", "Factoring Quadratics" ], "current_concepts": [ "Perfect-Square Trinomials", "Factoring Quadratics" ] } ## Define perfect-square trinomial form $$ (a \pm b)^2 = a^2 \pm 2ab + b^2 $$ ## Test each given expression $$ \begin{aligned} &\text{Option 1: } x^2 - 16x - 64 \implies b^2 = -64 \quad (\text{Not a perfect square over real numbers})\ &\text{Option 2: } 4x^2 + 12x + 9 = (2x)^2 + 2(2x)(3) + 3^2 = (2x + 3)^2 \quad (\text{Perfect-square trinomial})\ &\text{Option 3: } x^2 + 20x + 100 = x^2 + 2(x)(10) + 10^2 = (x + 10)^2 \quad (\text{Perfect-square trinomial})\ &\text{Option 4: } x^2 + 4x + 16 \implies 2ab = 2(x)(4) = 8x eq 4x \quad (\text{Not a perfect-square trinomial}) \end{aligned} $$ ## Identify the correct options $$ \text{Correct options: } 4x^2 + 12x + 9 \text{ and } x^2 + 20x + 100 $$

$x^2 - 16x - 64$

$4x^2 + 12x + 9$

$x^2 + 20x + 100$

$x^2 + 4x + 16$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Perfect-Square Trinomials" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Define perfect-square trinomial form

Test each given expression

Identify the correct options

Answer: