Answer :
We start with the expression
$$
\left(10f^2 - 12f + 7\right) - \left(-3f^2 - 5f + 11\right).
$$
**Step 1. Distribute the negative sign:**
When subtracting the second polynomial, we distribute the minus sign through each of its terms:
$$
10f^2 - 12f + 7 + 3f^2 + 5f - 11.
$$
**Step 2. Combine like terms:**
- For the $f^2$ terms:
$$10f^2 + 3f^2 = 13f^2.$$
- For the $f$ terms:
$$-12f + 5f = -7f.$$
- For the constant terms:
$$7 - 11 = -4.$$
**Step 3. Write the final expression:**
Putting it all together, we have
$$
13f^2 - 7f - 4.
$$
Thus, the final result is
$$\boxed{13f^2 - 7f -4}.$$
$$
\left(10f^2 - 12f + 7\right) - \left(-3f^2 - 5f + 11\right).
$$
**Step 1. Distribute the negative sign:**
When subtracting the second polynomial, we distribute the minus sign through each of its terms:
$$
10f^2 - 12f + 7 + 3f^2 + 5f - 11.
$$
**Step 2. Combine like terms:**
- For the $f^2$ terms:
$$10f^2 + 3f^2 = 13f^2.$$
- For the $f$ terms:
$$-12f + 5f = -7f.$$
- For the constant terms:
$$7 - 11 = -4.$$
**Step 3. Write the final expression:**
Putting it all together, we have
$$
13f^2 - 7f - 4.
$$
Thus, the final result is
$$\boxed{13f^2 - 7f -4}.$$
