which is equivalent to $(4xy - 3z)^2$, and what type of special product is it?

$16x^2y^2 + 9z^2$, the difference of squares
$16x^2y^2 + 9z^2$, a perfect square trinomial
$16x^2y^2 - 24xyz + 9z^2$, the difference of squares
$16x^2y^2 - 24xyz + 9z^2$, a perfect square trinomial

Question

which is equivalent to $(4xy - 3z)^2$, and what type of special product is it?

$16x^2y^2 + 9z^2$, the difference of squares
$16x^2y^2 + 9z^2$, a perfect square trinomial
$16x^2y^2 - 24xyz + 9z^2$, the difference of squares
$16x^2y^2 - 24xyz + 9z^2$, a perfect square trinomial

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 Trinomial", "Polynomial Multiplication" ], "current_concepts": [ "Perfect Square Trinomial", "Polynomial Multiplication" ] } ## Identify the algebraic form $$ (a - b)^2 = a^2 - 2ab + b^2 $$ ## Substitute the given terms $$ \begin{aligned} a &= 4xy \ b &= 3z \end{aligned} $$ ## Expand and simplify $$ \begin{aligned} (4xy - 3z)^2 &= (4xy)^2 - 2(4xy)(3z) + (3z)^2 \ &= 16x^2y^2 - 24xyz + 9z^2 \end{aligned} $$ This resulting three-term expression is a perfect square trinomial.

(A) $16x^2y^2+9z^2$, the difference of squares

(B) $16x^2y^2+9z^2$, a perfect square trinomial

(C) $16x^2y^2-24xyz+9z^2$, the difference of squares

(D) $16x^2y^2-24xyz+9z^2$, a perfect square trinomial

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

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Question

Explanation:

Identify the algebraic form

Substitute the given terms

Expand and simplify

Answer: