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].
[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].
