Sure! To solve this problem step-by-step, let's carefully simplify the given expression.
Given:
[tex]\[ \left(6m^5 + 3 - m^3 - 4m\right) - \left(-m^5 + 2m^3 - 4m + 6\right) \][/tex]
### Step 1: Write the subtraction as addition of the additive inverse
[tex]\[
\left(6m^5 + 3 - m^3 - 4m\right) + \left(m^5 - 2m^3 + 4m - 6\right)
\][/tex]
### Step 2: Rewrite terms that are subtracted as addition of the opposite
[tex]\[
6m^5 + 3 + (-m^3) + (-4m) + m^5 + (-2m^3) + 4m + (-6)
\][/tex]
### Step 3: Group like terms
[tex]\[
\begin{array}{l}
\text{Group } m^5: \quad (6m^5 + m^5) \\
\text{Group constants:} \quad (3 + (-6)) \\
\text{Group } m^3: \quad (-m^3 + (-2m^3)) \\
\text{Group } m: \quad (-4m + 4m)
\end{array}
\][/tex]
### Step 4: Combine like terms
Combining the like terms, we get:
[tex]\[
\begin{array}{l}
m^5: \quad 6m^5 + m^5 = 7m^5 \\
\text{Constants:} \quad 3 + (-6) = -3 \\
m^3: \quad -m^3 + (-2m^3) = -3m^3 \\
m: \quad -4m + 4m = 0m
\end{array}
\][/tex]
### Step 5: Write the resulting polynomial in standard form
Since the coefficient of [tex]\(m\)[/tex] is zero, we omit that term. Therefore, the resulting polynomial in standard form is:
[tex]\[
7m^5 - 3m^3 - 3
\][/tex]
So the final result is:
[tex]\[ 7m^5 - 3m^3 - 3 \][/tex]
