question 10

subtract the following polynomials: $(15n + 5n^7 + 14n^4) - (-2n^4 + 3n^7 + 2n)$

$2n^7 + 16n^4 + 13n$
$31n^{13}$
$2n^7 + 12n^4 + 13n$
$8n^7 + 12n^4 + 17n$

Question

question 10

subtract the following polynomials: $(15n + 5n^7 + 14n^4) - (-2n^4 + 3n^7 + 2n)$

$2n^7 + 16n^4 + 13n$
$31n^{13}$
$2n^7 + 12n^4 + 13n$
$8n^7 + 12n^4 + 17n$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Subtraction", "Distributive Property with Negative Sign", "Combining Like Terms" ], "new_concepts": [], "current_concepts": [ "Polynomial Subtraction", "Distributive Property with Negative Sign", "Combining Like Terms" ] } ## Distribute the negative sign $$ (15n + 5n^7 + 14n^4) - (-2n^4 + 3n^7 + 2n) = 15n + 5n^7 + 14n^4 + 2n^4 - 3n^7 - 2n $$ ## Group and combine like terms $$ \begin{aligned} (5n^7 - 3n^7) + (14n^4 + 2n^4) + (15n - 2n) &= (5 - 3)n^7 + (14 + 2)n^4 + (15 - 2)n\ &= 2n^7 + 16n^4 + 13n \end{aligned} $$

(A) $2n^7 + 16n^4 + 13n$

(B) $31n^{13}$

(C) $2n^7 + 12n^4 + 13n$

(D) $8n^7 + 12n^4 + 17n$

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

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QUESTION IMAGE

Question

Explanation:

Distribute the negative sign

Group and combine like terms

Answer: