Answer :
Sure, let's subtract the polynomials step-by-step:
We start with the given expression to subtract:
[tex]\[
(10 f^2 - 12 f + 7) - (-3 f^2 - 5 f + 11)
\][/tex]
Step 1: Distribute the negative sign to the terms inside the parentheses:
[tex]\[
10 f^2 - 12 f + 7 + 3 f^2 + 5 f - 11
\][/tex]
Step 2: Combine like terms:
- Combine the [tex]\( f^2 \)[/tex] terms:
[tex]\[
10 f^2 + 3 f^2 = 13 f^2
\][/tex]
- Combine the [tex]\( f \)[/tex] terms:
[tex]\[
-12 f + 5 f = -7 f
\][/tex]
- Combine the constant terms:
[tex]\[
7 - 11 = -4
\][/tex]
Step 3: Write down the resulting expression:
[tex]\[
13 f^2 - 7 f - 4
\][/tex]
Therefore, the answer to the subtraction problem is:
[tex]\[
13 f^2 - 7 f - 4
\][/tex]
So, the correct choice is:
[tex]\[
\boxed{13 f^2 - 7 f - 4}
\][/tex]
We start with the given expression to subtract:
[tex]\[
(10 f^2 - 12 f + 7) - (-3 f^2 - 5 f + 11)
\][/tex]
Step 1: Distribute the negative sign to the terms inside the parentheses:
[tex]\[
10 f^2 - 12 f + 7 + 3 f^2 + 5 f - 11
\][/tex]
Step 2: Combine like terms:
- Combine the [tex]\( f^2 \)[/tex] terms:
[tex]\[
10 f^2 + 3 f^2 = 13 f^2
\][/tex]
- Combine the [tex]\( f \)[/tex] terms:
[tex]\[
-12 f + 5 f = -7 f
\][/tex]
- Combine the constant terms:
[tex]\[
7 - 11 = -4
\][/tex]
Step 3: Write down the resulting expression:
[tex]\[
13 f^2 - 7 f - 4
\][/tex]
Therefore, the answer to the subtraction problem is:
[tex]\[
13 f^2 - 7 f - 4
\][/tex]
So, the correct choice is:
[tex]\[
\boxed{13 f^2 - 7 f - 4}
\][/tex]
