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Answer :
Let's solve the expression step by step:
We have two expressions to add:
1. [tex]\(3x^4 + 2x^3 - 7\)[/tex]
2. [tex]\(4x^6 - 5x^3 + 9\)[/tex]
The goal is to combine these by adding like terms:
1. Identify terms by their degrees:
- The terms from the first expression are: [tex]\(3x^4\)[/tex], [tex]\(2x^3\)[/tex], and [tex]\(-7\)[/tex].
- The terms from the second expression are: [tex]\(4x^6\)[/tex], [tex]\(-5x^3\)[/tex], and [tex]\(9\)[/tex].
2. Combine like terms:
- [tex]\(x^6\)[/tex] terms: There is only one term, [tex]\(4x^6\)[/tex].
- [tex]\(x^4\)[/tex] terms: There is only one term, [tex]\(3x^4\)[/tex].
- [tex]\(x^3\)[/tex] terms: Combine [tex]\(2x^3\)[/tex] and [tex]\(-5x^3\)[/tex]:
[tex]\[
2x^3 - 5x^3 = -3x^3
\][/tex]
- Constant terms: Combine [tex]\(-7\)[/tex] and [tex]\(9\)[/tex]:
[tex]\[
-7 + 9 = 2
\][/tex]
3. Write the combined expression:
- The combined expression becomes:
[tex]\[
4x^6 + 3x^4 - 3x^3 + 2
\][/tex]
4. Compare with the given choices:
- Option A: [tex]\(4x^6 + 3x^4 - 3x^3 + 2\)[/tex]
- Option B: [tex]\(4x^6 + 3x^4 + 7x^3 + 2\)[/tex]
- Option C: [tex]\(4x^6 + 3x^4 - 5x^3 + 2\)[/tex]
- Option D: [tex]\(7x^{10} - 3x^3 + 2\)[/tex]
The combined expression matches Option A: [tex]\(4x^6 + 3x^4 - 3x^3 + 2\)[/tex].
So, the correct answer is A.
We have two expressions to add:
1. [tex]\(3x^4 + 2x^3 - 7\)[/tex]
2. [tex]\(4x^6 - 5x^3 + 9\)[/tex]
The goal is to combine these by adding like terms:
1. Identify terms by their degrees:
- The terms from the first expression are: [tex]\(3x^4\)[/tex], [tex]\(2x^3\)[/tex], and [tex]\(-7\)[/tex].
- The terms from the second expression are: [tex]\(4x^6\)[/tex], [tex]\(-5x^3\)[/tex], and [tex]\(9\)[/tex].
2. Combine like terms:
- [tex]\(x^6\)[/tex] terms: There is only one term, [tex]\(4x^6\)[/tex].
- [tex]\(x^4\)[/tex] terms: There is only one term, [tex]\(3x^4\)[/tex].
- [tex]\(x^3\)[/tex] terms: Combine [tex]\(2x^3\)[/tex] and [tex]\(-5x^3\)[/tex]:
[tex]\[
2x^3 - 5x^3 = -3x^3
\][/tex]
- Constant terms: Combine [tex]\(-7\)[/tex] and [tex]\(9\)[/tex]:
[tex]\[
-7 + 9 = 2
\][/tex]
3. Write the combined expression:
- The combined expression becomes:
[tex]\[
4x^6 + 3x^4 - 3x^3 + 2
\][/tex]
4. Compare with the given choices:
- Option A: [tex]\(4x^6 + 3x^4 - 3x^3 + 2\)[/tex]
- Option B: [tex]\(4x^6 + 3x^4 + 7x^3 + 2\)[/tex]
- Option C: [tex]\(4x^6 + 3x^4 - 5x^3 + 2\)[/tex]
- Option D: [tex]\(7x^{10} - 3x^3 + 2\)[/tex]
The combined expression matches Option A: [tex]\(4x^6 + 3x^4 - 3x^3 + 2\)[/tex].
So, the correct answer is A.
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