which quadratic expression represents the product of these factors?

$(2x + 5)(7 - 4x)$

- $-8x^2 - 6x + 35$
- $-8x^2 + 34x - 35$
- $-8x^2 - 34x + 35$
- $-8x^2 + 6x - 35$

Question

which quadratic expression represents the product of these factors?

$(2x + 5)(7 - 4x)$

- $-8x^2 - 6x + 35$
- $-8x^2 + 34x - 35$
- $-8x^2 - 34x + 35$
- $-8x^2 + 6x - 35$

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": [ "Distributive Property", "Combining Like Terms", "Polynomial Simplification" ], "new_concepts": [ "Multiplying Binomials" ], "current_concepts": [ "Distributive Property", "Combining Like Terms", "Polynomial Simplification", "Multiplying Binomials" ] } ## Apply the distributive property Using the *Distributive Property* knowledge point $$ \begin{aligned} (2x + 5)(7 - 4x) &= 2x(7 - 4x) + 5(7 - 4x) \ &= 14x - 8x^2 + 35 - 20x \end{aligned} $$ ## Combine like terms Using the *Combining Like Terms* and *Polynomial Simplification* knowledge points $$ \begin{aligned} 14x - 8x^2 + 35 - 20x &= -8x^2 + (14x - 20x) + 35 \ &= -8x^2 - 6x + 35 \end{aligned} $$

(A) $-8x^2 - 6x + 35$

(B) $-8x^2 + 34x - 35$

(C) $-8x^2 - 34x + 35$

(D) $-8x^2 + 6x - 35$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Operations" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the distributive property

Combine like terms

Answer: