To find the difference of the polynomials given by [tex]\( m^2 n^2 - 7 \)[/tex] and [tex]\( m n + 4 \)[/tex], we will subtract the second polynomial from the first one.
Let's write the expression we need to evaluate:
[tex]\[
(m^2 n^2 - 7) - (m n + 4)
\][/tex]
Now, distribute the minus sign across the second polynomial:
[tex]\[
m^2 n^2 - 7 - m n - 4
\][/tex]
Next, combine the like terms:
[tex]\[
m^2 n^2 - m n - 7 - 4
\][/tex]
Simplify the constants by adding [tex]\(-7\)[/tex] and [tex]\(-4\)[/tex]:
[tex]\[
m^2 n^2 - m n - 11
\][/tex]
Thus, the difference of the polynomials is:
[tex]\[
\boxed{m^2 n^2 - m n - 11}
\][/tex]
