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Answer :
We want to subtract
[tex]$$
\left(10f^2 - 12f + 7\right) - \left(-3f^2 - 5f + 11\right).
$$[/tex]
Step 1. Remove the parentheses by distributing the negative sign. This means changing the signs of each term in the second polynomial:
[tex]$$
(10f^2 - 12f + 7) + (3f^2 + 5f - 11).
$$[/tex]
Step 2. Combine like terms by adding the coefficients of the corresponding powers of [tex]$f$[/tex].
For the [tex]$f^2$[/tex] terms:
[tex]$$
10f^2 + 3f^2 = 13f^2.
$$[/tex]
For the [tex]$f$[/tex] terms:
[tex]$$
-12f + 5f = -7f.
$$[/tex]
For the constant terms:
[tex]$$
7 - 11 = -4.
$$[/tex]
Step 3. Write down the resulting polynomial:
[tex]$$
13f^2 - 7f - 4.
$$[/tex]
Thus, the answer is:
[tex]$$
13f^2 - 7f - 4.
$$[/tex]
[tex]$$
\left(10f^2 - 12f + 7\right) - \left(-3f^2 - 5f + 11\right).
$$[/tex]
Step 1. Remove the parentheses by distributing the negative sign. This means changing the signs of each term in the second polynomial:
[tex]$$
(10f^2 - 12f + 7) + (3f^2 + 5f - 11).
$$[/tex]
Step 2. Combine like terms by adding the coefficients of the corresponding powers of [tex]$f$[/tex].
For the [tex]$f^2$[/tex] terms:
[tex]$$
10f^2 + 3f^2 = 13f^2.
$$[/tex]
For the [tex]$f$[/tex] terms:
[tex]$$
-12f + 5f = -7f.
$$[/tex]
For the constant terms:
[tex]$$
7 - 11 = -4.
$$[/tex]
Step 3. Write down the resulting polynomial:
[tex]$$
13f^2 - 7f - 4.
$$[/tex]
Thus, the answer is:
[tex]$$
13f^2 - 7f - 4.
$$[/tex]
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