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Answer :
To solve the problem of subtracting the given polynomials [tex]\((10f^2 - 12f + 7) - (-3f^2 - 5f + 11)\)[/tex], let's follow these steps:
1. Distribute the Negative Sign:
The expression we are subtracting is [tex]\((-3f^2 - 5f + 11)\)[/tex]. Distributing the negative sign to each term, we get:
[tex]\[
-(-3f^2) - (-5f) - 11 = 3f^2 + 5f - 11
\][/tex]
2. Write Down the Original Expression:
The original polynomial expression is [tex]\(10f^2 - 12f + 7\)[/tex].
3. Perform the Subtraction:
Now, we need to subtract the modified second polynomial from the first. This can be done by subtracting the corresponding coefficients of each term:
- For [tex]\(f^2\)[/tex] terms:
[tex]\(10f^2 - 3f^2 = 7f^2\)[/tex]
- For [tex]\(f\)[/tex] terms:
[tex]\(-12f - 5f = -17f\)[/tex]
- For the constant terms:
[tex]\(7 - (-11) = 7 + 11 = 18\)[/tex]
4. Combine the Results:
Putting all the resulting terms together, the simplified expression becomes:
[tex]\[
7f^2 - 17f + 18
\][/tex]
Thus, the correct result of subtracting the polynomials is [tex]\(7f^2 - 17f + 18\)[/tex].
1. Distribute the Negative Sign:
The expression we are subtracting is [tex]\((-3f^2 - 5f + 11)\)[/tex]. Distributing the negative sign to each term, we get:
[tex]\[
-(-3f^2) - (-5f) - 11 = 3f^2 + 5f - 11
\][/tex]
2. Write Down the Original Expression:
The original polynomial expression is [tex]\(10f^2 - 12f + 7\)[/tex].
3. Perform the Subtraction:
Now, we need to subtract the modified second polynomial from the first. This can be done by subtracting the corresponding coefficients of each term:
- For [tex]\(f^2\)[/tex] terms:
[tex]\(10f^2 - 3f^2 = 7f^2\)[/tex]
- For [tex]\(f\)[/tex] terms:
[tex]\(-12f - 5f = -17f\)[/tex]
- For the constant terms:
[tex]\(7 - (-11) = 7 + 11 = 18\)[/tex]
4. Combine the Results:
Putting all the resulting terms together, the simplified expression becomes:
[tex]\[
7f^2 - 17f + 18
\][/tex]
Thus, the correct result of subtracting the polynomials is [tex]\(7f^2 - 17f + 18\)[/tex].
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