b) $4xy^2 + 3xy - 6x - 2xy^2 + 5xy + 4y$

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Polynomial Simplification", "Combining Like Terms" ], "new_concepts": [], "current_concepts": [ "Polynomial Simplification", "Combining Like Terms" ] } ## Identify the terms of the expression We begin with the given algebraic expression: $$ 4xy^2 + 3xy - 6x - 2xy^2 + 5xy + 4y $$ ## Group the like terms Using the **Combining Like Terms** and **Polynomial Simplification** knowledge points $$ \begin{aligned} &\text{Group } xy^2 \text{ terms: } (4xy^2 - 2xy^2) \ &\text{Group } xy \text{ terms: } (3xy + 5xy) \ &\text{Group } x \text{ terms: } -6x \ &\text{Group } y \text{ terms: } 4y \end{aligned} $$ ## Combine the coefficients Using the **Polynomial Simplification** knowledge point $$ \begin{aligned} &(4 - 2)xy^2 + (3 + 5)xy - 6x + 4y \ &= 2xy^2 + 8xy - 6x + 4y \end{aligned} $$ $2xy^2 + 8xy - 6x + 4y$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Simplification" ] }

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Question

Explanation:

Identify the terms of the expression

Group the like terms

Combine the coefficients

Answer: