find the difference.

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

$?x^2 + \box x + \box$

Question

find the difference.

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

$?x^2 + \box x + \box$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Distributive Property", "Algebraic Simplification" ], "new_concepts": [ "Polynomial Subtraction", "Combining Like Terms" ], "current_concepts": [ "Distributive Property", "Algebraic Simplification", "Polynomial Subtraction", "Combining Like Terms" ] } ## Distribute the negative sign Using the *Distributive Property* knowledge point $$ -(2x^2 + 2x - 3) = -2x^2 - 2x + 3 $$ ## Rewrite the entire expression Using the *Algebraic Simplification* knowledge point $$ (x^2 - 4x - 2) - (2x^2 + 2x - 3) = x^2 - 4x - 2 - 2x^2 - 2x + 3 $$ ## Group and combine like terms Using the *Algebraic Simplification* knowledge point $$ \begin{aligned} (x^2 - 2x^2) + (-4x - 2x) + (-2 + 3) &= (1 - 2)x^2 + (-4 - 2)x + 1 \ &= -1x^2 + (-6)x + 1 \ &= -x^2 - 6x + 1 \end{aligned} $$ Find the difference. $$(x^2 - 4x - 2) - (2x^2 + 2x - 3)$$ $-1$$x^2 +$ $-6$$x +$ $1$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Subtraction" ] }

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QUESTION IMAGE

Question

Explanation:

Distribute the negative sign

Rewrite the entire expression

Group and combine like terms

Answer: