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Subtract:

[tex]\[

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

\][/tex]

Choose the correct result:

A. [tex]\(7f^2 - 17f - 4\)[/tex]

B. [tex]\(13f^2 - 17f - 4\)[/tex]

C. [tex]\(13f^2 - 7f - 4\)[/tex]

D. [tex]\(7f^2 - 17f + 18\)[/tex]

Answer :

To solve the subtraction problem:

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

we'll follow these steps:

1. Distribute the Negative Sign: When subtracting a polynomial, distribute the negative sign to each term in the second polynomial:

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

2. Combine Like Terms: Add the corresponding terms from each polynomial together:

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

3. Write the Resulting Polynomial:

[tex]\[
13 f^2 - 7 f - 4
\][/tex]

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

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