To determine the difference between the polynomials [tex]\((m^2 n^2 - 7)\)[/tex] and [tex]\((m n + 4)\)[/tex], follow these steps to perform the subtraction:
1. Write down the given polynomials:
[tex]\[
P1 = m^2 n^2 - 7
\][/tex]
[tex]\[
P2 = m n + 4
\][/tex]
2. Subtract the second polynomial [tex]\(P2\)[/tex] from the first polynomial [tex]\(P1\)[/tex]:
[tex]\[
\text{Difference} = P1 - P2
\][/tex]
[tex]\[
\text{Difference} = (m^2 n^2 - 7) - (m n + 4)
\][/tex]
3. Distribute the subtraction across the terms in [tex]\(P2\)[/tex]:
[tex]\[
\text{Difference} = m^2 n^2 - 7 - m n - 4
\][/tex]
4. Combine like terms:
- Combine the constant terms [tex]\(-7\)[/tex] and [tex]\(-4\)[/tex]:
[tex]\[
-7 - 4 = -11
\][/tex]
- The polynomial does not have any more like terms to combine.
5. Resultant polynomial:
[tex]\[
\text{Difference} = m^2 n^2 - m n - 11
\][/tex]
Thus, the difference of the polynomials [tex]\( \left(m^2 n^2 - 7\right) - \left(m n + 4\right) \)[/tex] is:
[tex]\[
m^2 n^2 - m n - 11
\][/tex]
Therefore, the correct answer from the given options is:
[tex]\[
\boxed{m^2 n^2 - m n - 11}
\][/tex]
