Question

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.

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

1. rewrite terms that are subtracted as addition of the opposite.

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

1. group like terms.

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

1. combine like terms.
2. write the resulting polynomial in standard form.

\boxed{} $m^5 - $ \boxed{} $m^3 + $ \boxed{} $m - 3$

Explanation:

Step1: Combine $m^5$ terms

$(6m^5 + m^5) = 7m^5$

Step2: Combine $m^3$ terms

$(-m^3 -2m^3) = -3m^3$

Step3: Combine $m$ terms

$(-4m + 4m) = 0m$

Step4: Combine constant terms

$(3 - 6) = -3$

Step5: Write in standard form

Arrange terms by descending degree.

Answer:

$7m^5 - 3m^3 + 0m - 3$

The blanks (in order) are 7, 3, 0.