select the correct answer.

which expression is equivalent to the given polynomial expression?
$(-4a^2 - 3b) + (-2ab - a^2 + b^2) + (-b^2 + 6ab)$

$\bigcirc -3a^2 + 4ab + 3b$
$\bigcirc -3a^2 + 2b^2 + 8ab + 3b$
$\bigcirc -5a^2 + 2b^2 + 8ab + 3b$
$\bigcirc -5a^2 + 4ab - 3b$

Question

select the correct answer.

which expression is equivalent to the given polynomial expression?
$(-4a^2 - 3b) + (-2ab - a^2 + b^2) + (-b^2 + 6ab)$

$\bigcirc -3a^2 + 4ab + 3b$
$\bigcirc -3a^2 + 2b^2 + 8ab + 3b$
$\bigcirc -5a^2 + 2b^2 + 8ab + 3b$
$\bigcirc -5a^2 + 4ab - 3b$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Operations", "Like Terms" ], "new_concepts": [], "current_concepts": [ "Polynomial Operations", "Like Terms" ] } ## Remove parentheses and group like terms $$ (-4a^2 - 3b) + (-2ab - a^2 + b^2) + (-b^2 + 6ab) = -4a^2 - 3b - 2ab - a^2 + b^2 - b^2 + 6ab $$ ## Combine like terms $$ \begin{aligned} a^2\text{ terms: } & -4a^2 - a^2 = -5a^2 \ ab\text{ terms: } & -2ab + 6ab = 4ab \ b^2\text{ terms: } & b^2 - b^2 = 0 \ b\text{ terms: } & -3b \end{aligned} $$ ## Write the simplified expression $$ -5a^2 + 4ab - 3b $$

(A) $-3a^2 + 4ab + 3b$

(B) $-3a^2 + 2b^2 + 8ab + 3b$

(C) $-5a^2 + 2b^2 + 8ab + 3b$

(D) $-5a^2 + 4ab - 3b$

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

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QUESTION IMAGE

Question

Explanation:

Remove parentheses and group like terms

Combine like terms

Write the simplified expression

Answer: