select the correct answer.

which expression is equivalent to the given polynomial expression?
$(9mn - 19m^4n) - (8m^2 + 12m^4n + 9mn)$

$-31m^4n - 8m^2$
$-7m^4n + 8m^2$
$-7m^4n + 18mn - 8m^2$
$-31m^4n + 18mn - 8m^2$

Question

select the correct answer.

which expression is equivalent to the given polynomial expression?
$(9mn - 19m^4n) - (8m^2 + 12m^4n + 9mn)$

$-31m^4n - 8m^2$
$-7m^4n + 8m^2$
$-7m^4n + 18mn - 8m^2$
$-31m^4n + 18mn - 8m^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Addition", "Combining Like Terms", "Distributive Property" ], "new_concepts": [], "current_concepts": [ "Polynomial Addition", "Combining Like Terms", "Distributive Property" ] } ## Distribute the negative sign $$ (9mn - 19m^4n) - (8m^2 + 12m^4n + 9mn) = 9mn - 19m^4n - 8m^2 - 12m^4n - 9mn $$ ## Group and combine like terms $$ \begin{aligned} &= (-19m^4n - 12m^4n) + (9mn - 9mn) - 8m^2 \ &= -31m^4n + 0 - 8m^2 \ &= -31m^4n - 8m^2 \end{aligned} $$

(A) $-31m^4n - 8m^2$

(B) $-7m^4n + 8m^2$

(C) $-7m^4n + 18mn - 8m^2$

(D) $-31m^4n + 18mn - 8m^2$

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

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QUESTION IMAGE

Question

Explanation:

Distribute the negative sign

Group and combine like terms

Answer: