Answer :
Let's solve the subtraction problem step by step:
We want to subtract the expression [tex]\((-3 f^2 - 5 f + 11)\)[/tex] from the expression [tex]\((10 f^2 - 12 f + 7)\)[/tex].
Here's how we do it:
1. Write the original subtraction expression:
[tex]\((10 f^2 - 12 f + 7) - (-3 f^2 - 5 f + 11)\)[/tex]
2. Distribute the negative sign to the second expression:
[tex]\((10 f^2 - 12 f + 7) + (3 f^2 + 5 f - 11)\)[/tex]
Notice that the signs in the second expression have changed because we are subtracting each term.
3. Combine like terms:
- For the [tex]\(f^2\)[/tex] terms:
[tex]\[
10 f^2 + 3 f^2 = 13 f^2
\][/tex]
- For the [tex]\(f\)[/tex] terms:
[tex]\[
-12 f + 5 f = -7 f
\][/tex]
- For the constant terms:
[tex]\[
7 - 11 = -4
\][/tex]
4. Compile the results:
The simplified expression is:
[tex]\[
13 f^2 - 7 f - 4
\][/tex]
Therefore, the result of the subtraction is [tex]\(13 f^2 - 7 f - 4\)[/tex].
We want to subtract the expression [tex]\((-3 f^2 - 5 f + 11)\)[/tex] from the expression [tex]\((10 f^2 - 12 f + 7)\)[/tex].
Here's how we do it:
1. Write the original subtraction expression:
[tex]\((10 f^2 - 12 f + 7) - (-3 f^2 - 5 f + 11)\)[/tex]
2. Distribute the negative sign to the second expression:
[tex]\((10 f^2 - 12 f + 7) + (3 f^2 + 5 f - 11)\)[/tex]
Notice that the signs in the second expression have changed because we are subtracting each term.
3. Combine like terms:
- For the [tex]\(f^2\)[/tex] terms:
[tex]\[
10 f^2 + 3 f^2 = 13 f^2
\][/tex]
- For the [tex]\(f\)[/tex] terms:
[tex]\[
-12 f + 5 f = -7 f
\][/tex]
- For the constant terms:
[tex]\[
7 - 11 = -4
\][/tex]
4. Compile the results:
The simplified expression is:
[tex]\[
13 f^2 - 7 f - 4
\][/tex]
Therefore, the result of the subtraction is [tex]\(13 f^2 - 7 f - 4\)[/tex].
