Find:
[tex]\left(6 m^5+3-m^3-4 m\right)-\left(-m^5+2 m^3-4 m+6\right)[/tex]
1. Write subtraction of a polynomial expression as addition of the additive inverse:
[tex]\left(6 m^5+3-m^3-4 m\right)+\left(m^5-2 m^3+4 m-6\right)[/tex]
2. Rewrite terms that are subtracted as addition of the opposite:
[tex]6 m^5+3+\left(-m^3\right)+(-4 m)+m^5+\left(-2 m^3\right)+4 m+(-6)[/tex]
3. Group like terms:
[tex]\left[6 m^5+m^5\right]+[3+(-6)]+\left[\left(-m^3\right)+\left(-2 m^3\right)\right]+[(-4 m)+4 m][/tex]
4. Combine like terms.
5. Write the resulting polynomial in standard form:
[tex]\square \ m^5 \ \square \ m^3 \ +\ \square \ m \ -\ 3[/tex]