High School

Subtract:

[tex]\left(10f^2 - 12f + 7\right) - \left(-3f^2 - 5f + 11\right)[/tex]

A. [tex]13f^2 - 7f - 4[/tex]
B. [tex]7f^2 - 17f + 18[/tex]
C. [tex]13f^2 - 17f - 4[/tex]
D. [tex]7f^2 - 17f - 4[/tex]

Answer :

To solve the subtraction problem [tex]\((10 f^2 - 12 f + 7) - (-3 f^2 - 5 f + 11)\)[/tex], follow these steps:

1. Rewrite the Expression:
Start by writing the expression as it is with the subtraction sign:
[tex]\[
(10 f^2 - 12 f + 7) - (-3 f^2 - 5 f + 11)
\][/tex]

2. Distribute the Negative Sign:
Remove the parenthesis by distributing the negative sign to each term in the second expression:
[tex]\[
10 f^2 - 12 f + 7 + 3 f^2 + 5 f - 11
\][/tex]

3. Combine Like Terms:
Group the like terms together.

- For [tex]\(f^2\)[/tex] terms: [tex]\(10 f^2 + 3 f^2 = 13 f^2\)[/tex]
- For [tex]\(f\)[/tex] terms: [tex]\(-12 f + 5 f = -7 f\)[/tex]
- For constant terms: [tex]\(7 - 11 = -4\)[/tex]

4. Write the Simplified Expression:
After combining all like terms, the simplified expression is:
[tex]\[
13 f^2 - 7 f - 4
\][/tex]

So, the result of the subtraction is [tex]\(\boxed{13 f^2 - 7 f - 4}\)[/tex].