Sure! Let's take it step by step to solve the subtraction of the given polynomials:
[tex]\[ \left(3m^3 - 6\right) - \left(2m^3 - m^2 - 3\right) \][/tex]
1. Distribute the negative sign over the second polynomial:
[tex]\[ = 3m^3 - 6 - (2m^3 - m^2 - 3) \][/tex]
[tex]\[ = 3m^3 - 6 - 2m^3 + m^2 + 3 \][/tex]
2. Combine the like terms:
- For [tex]\(m^3\)[/tex] terms:
[tex]\[ 3m^3 - 2m^3 = m^3 \][/tex]
- For [tex]\(m^2\)[/tex] terms:
[tex]\[ m^2 \][/tex] (There are no other [tex]\(m^2\)[/tex] terms to combine with)
- For the constant terms:
[tex]\[ -6 + 3 = -3 \][/tex]
3. Combine all the simplified terms:
[tex]\[ m^3 + m^2 - 3 \][/tex]
So, the result of the subtraction is:
[tex]\[ \boxed{m^3 + m^2 - 3} \][/tex]
