subtracting polynomial expressions

find: $(6m^5 + 3 - m^3 - 4m) - (-m^5 + 2m^3 - 4m + 6)$

1. write subtraction of a polynomial expression as addition of the additive inverse.
$(6m^5 + 3 - m^3 - 4m) + (m^5 - 2m^3 + 4m - 6)$

2. rewrite terms that are subtracted as addition of the opposite.
$6m^5 + 3 + (-m^3) + (-4m) + m^5 + (-2m^3) + 4m + (-6)$

3. group like terms.
$6m^5 + m^5 + 3 + (-6) + (-m^3) + (-2m^3) + (-4m) + 4m$

4. combine like terms.

5. write the resulting polynomial in standard form.

$\box m^5 - \box m^3 + \box m - 3$

Question

subtracting polynomial expressions

find: $(6m^5 + 3 - m^3 - 4m) - (-m^5 + 2m^3 - 4m + 6)$

1. write subtraction of a polynomial expression as addition of the additive inverse.
$(6m^5 + 3 - m^3 - 4m) + (m^5 - 2m^3 + 4m - 6)$

2. rewrite terms that are subtracted as addition of the opposite.
$6m^5 + 3 + (-m^3) + (-4m) + m^5 + (-2m^3) + 4m + (-6)$

3. group like terms.
$6m^5 + m^5 + 3 + (-6) + (-m^3) + (-2m^3) + (-4m) + 4m$

4. combine like terms.

5. write the resulting polynomial in standard form.

$\box m^5 - \box m^3 + \box m - 3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Addition", "Additive Inverse" ], "new_concepts": [ "Polynomial Subtraction" ], "current_concepts": [ "Polynomial Subtraction", "Polynomial Addition", "Additive Inverse" ] } ## Group and combine like terms $$ \begin{aligned} &[6m^5 + m^5] + [3 + (-6)] + [(-m^3) + (-2m^3)] + [(-4m) + 4m]\ &= 7m^5 - 3 - 3m^3 + 0m \end{aligned} $$ ## Write in standard form $$ 7m^5 - 3m^3 + 0m - 3 $$ Write the resulting polynomial in standard form. 7$m^5 -$ 3$m^3 +$ 0$m - 3$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Subtraction" ] }

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Question

Explanation:

Group and combine like terms

Write in standard form

Answer: