which are perfect square trinomials? select two options.

$x^2 - 9$

$x^2 - 100$

$x^2 - 4x + 4$

$x^2 + 10x + 25$

$x^2 + 15x + 36$

Question

which are perfect square trinomials? select two options.

$x^2 - 9$

$x^2 - 100$

$x^2 - 4x + 4$

$x^2 + 10x + 25$

$x^2 + 15x + 36$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Perfect Square Trinomial" ], "new_concepts": [], "current_concepts": [ "Perfect Square Trinomial", "Factoring Polynomials" ] } ## Define perfect square trinomials Using the *Perfect Square Trinomial* knowledge point $$ (a \pm b)^2 = a^2 \pm 2ab + b^2 $$ ## Analyze binomial options Using the *Perfect Square Trinomial* knowledge point $$ \begin{aligned} &x^2 - 9 = (x - 3)(x + 3) \quad \text{(Difference of Squares)} \ &x^2 - 100 = (x - 10)(x + 10) \quad \text{(Difference of Squares)} \end{aligned} $$ ## Analyze trinomial options Using the *Perfect Square Trinomial* knowledge point $$ \begin{aligned} &x^2 - 4x + 4 = x^2 - 2(x)(2) + 2^2 = (x - 2)^2 \ &x^2 + 10x + 25 = x^2 + 2(x)(5) + 5^2 = (x + 5)^2 \ &x^2 + 15x + 36 = (x + 12)(x + 3) \end{aligned} $$

$x^2 - 9$

$x^2 - 100$

$x^2 - 4x + 4$

$x^2 + 10x + 25$

$x^2 + 15x + 36$

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

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Explanation:

Define perfect square trinomials

Analyze binomial options

Analyze trinomial options

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