what is the simplified form of this expression?

$(5x^2 + 2x + 11) - (7 + 4x - 2x^2)$

$\bigcirc$ $3x^2 + 6x + 4$
$\bigcirc$ $7x^2 - 2x + 4$
$\bigcirc$ $9 - 2x - 2x^2$
$\bigcirc$ $3x^2 - 2x + 4$

Question

what is the simplified form of this expression?

$(5x^2 + 2x + 11) - (7 + 4x - 2x^2)$

$\bigcirc$ $3x^2 + 6x + 4$
$\bigcirc$ $7x^2 - 2x + 4$
$\bigcirc$ $9 - 2x - 2x^2$
$\bigcirc$ $3x^2 - 2x + 4$

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": [], "current_concepts": [ "Distributive Property", "Combining Like Terms", "Polynomial Simplification" ] } ## Distribute the negative sign Using the *Distributive Property* knowledge point $$ -(7 + 4x - 2x^2) = -7 - 4x + 2x^2 $$ ## Rewrite the full expression Using the *Polynomial Simplification* knowledge point $$ (5x^2 + 2x + 11) - (7 + 4x - 2x^2) = 5x^2 + 2x + 11 - 7 - 4x + 2x^2 $$ ## Group and combine like terms Using the *Combining Like Terms* knowledge point $$ \begin{aligned} (5x^2 + 2x^2) + (2x - 4x) + (11 - 7) &= (5 + 2)x^2 + (2 - 4)x + (11 - 7) \ &= 7x^2 - 2x + 4 \end{aligned} $$

(A) $3x^2 + 6x + 4$

(B) $7x^2 - 2x + 4$

(C) $9 - 2x - 2x^2$

(D) $3x^2 - 2x + 4$

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

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QUESTION IMAGE

Question

Explanation:

Distribute the negative sign

Rewrite the full expression

Group and combine like terms

Answer: