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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].
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].
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