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{ "quality": "incomplete", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Multiplying Binomials", "FOIL Method", "Volume of Rectangular Prisms", "Algebraic Volume Expressions" ], "new_concepts": [], "current_concepts": [ "Multiplying Binomials", "FOIL Method", "Volume of Rectangular Prisms", "Algebraic Volume Expressions" ] } ## Identify the dimensions from the options The options represent the volume of a rectangular prism, which is the product of three linear dimensions: length, width, and height. Let the dimensions be $x$, $2x + 3$, and $4x + 1$. ## Calculate the product of the dimensions $$ \begin{aligned} V &= x(2x + 3)(4x + 1) \ &= x(8x^2 + 2x + 12x + 3) \ &= x(8x^2 + 14x + 3) \ &= 8x^3 + 14x^2 + 3x \end{aligned} $$ ## Match with the given options The calculated expression $8x^3 + 14x^2 + 3x$ matches the fourth option.

(A) $8x^2 + 9x + 3$

(B) $8x^2 + 14x + 3$

(C) $8x^3 + 9x^2 + 3x$

(D) $8x^3 + 14x^2 + 3x$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Multiplying Polynomials" ] }

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Explanation:

Identify the dimensions from the options

Calculate the product of the dimensions

Match with the given options

Answer: