which is equivalent to $(9y^2 - 4x)(9y^2 + 4x)$, and what type of special product is it?

$81y^4 - 16x^2$, a perfect square trinomial
$81y^4 - 16x^2$, the difference of squares
$81y^4 - 72xy^2 - 16x^2$, a perfect square trinomial
$81y^4 - 72xy^2 - 16x^2$, the difference of squares

Question

which is equivalent to $(9y^2 - 4x)(9y^2 + 4x)$, and what type of special product is it?

$81y^4 - 16x^2$, a perfect square trinomial
$81y^4 - 16x^2$, the difference of squares
$81y^4 - 72xy^2 - 16x^2$, a perfect square trinomial
$81y^4 - 72xy^2 - 16x^2$, the difference of squares

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Difference of Squares", "Polynomial Multiplication" ], "new_concepts": [], "current_concepts": [ "Difference of Squares", "Polynomial Multiplication", "Perfect Square Trinomial" ] } ## Identify the special product pattern $$ (a - b)(a + b) = a^2 - b^2 $$ ## Substitute the given terms $$ \begin{aligned} a &= 9y^2 \ b &= 4x \end{aligned} $$ ## Calculate the final simplified expression $$ (9y^2)^2 - (4x)^2 = 81y^4 - 16x^2 $$

(A) $81y^4-16x^2$, a perfect square trinomial

(B) $81y^4-16x^2$, the difference of squares

(C) $81y^4-72xy^2-16x^2$, a perfect square trinomial

(D) $81y^4-72xy^2-16x^2$, the difference of squares

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Difference of Squares" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the special product pattern

Substitute the given terms

Calculate the final simplified expression

Answer: