What is the difference of the polynomials? (m^2n^2 - 7) - (mn + 4)

1. Distribute the negative sign: The problem asks for the difference between two polynomials. This means we need to subtract the second polynomial from the first. When subtracting a polynomial, we distribute the negative sign to each term within the parentheses of the second polynomial. So, $-(mn + 4)$ becomes $-mn - 4$.

The expression is now: $m^2n^2 - 7 - mn - 4$.

2. Combine like terms: Now, we look for terms that have the same variables raised to the same powers. In this expression, we have:
- A term with $m^2n^2$: $m^2n^2$
- A term with $mn$: $-mn$
- Constant terms: $-7$ and $-4$

Combine the constant terms: $-7 - 4 = -11$.

1. Write the simplified polynomial: Combine the results from the previous step to write the final simplified polynomial.

The simplified expression is $m^2n^2 - mn - 11$.