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Answer :
To find the simplest form of the expression [tex]\((4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x)\)[/tex], we need to combine like terms. Let's go through the process step-by-step:
1. Identify the like terms:
- Terms with [tex]\(x^3\)[/tex]: [tex]\(4x^3\)[/tex] and [tex]\(3x^3\)[/tex]
- Terms with [tex]\(x^2\)[/tex]: There is no [tex]\(x^2\)[/tex] term in the first expression, and [tex]\(-5x^2\)[/tex] from the second expression.
- Terms with [tex]\(x\)[/tex]: [tex]\(6x\)[/tex] and [tex]\(-5x\)[/tex]
- Constant term: [tex]\(-7\)[/tex]
2. Combine the like terms:
- For [tex]\(x^3\)[/tex]:
- [tex]\(4x^3 + 3x^3 = 7x^3\)[/tex]
- For [tex]\(x^2\)[/tex]:
- Since there is no [tex]\(x^2\)[/tex] term in the first expression, we take [tex]\(-5x^2\)[/tex] from the second one, resulting in [tex]\(-5x^2\)[/tex].
- For [tex]\(x\)[/tex]:
- [tex]\(6x - 5x = x\)[/tex]
- For the constant term:
- [tex]\(-7\)[/tex] stays [tex]\(-7\)[/tex], as it's just a constant term.
3. Write the combined expression:
Putting it all together, the expression in its simplest form is:
[tex]\[
7x^3 - 5x^2 + x - 7
\][/tex]
So, the correct choice is [tex]\(7x^3 - 5x^2 + x - 7\)[/tex].
1. Identify the like terms:
- Terms with [tex]\(x^3\)[/tex]: [tex]\(4x^3\)[/tex] and [tex]\(3x^3\)[/tex]
- Terms with [tex]\(x^2\)[/tex]: There is no [tex]\(x^2\)[/tex] term in the first expression, and [tex]\(-5x^2\)[/tex] from the second expression.
- Terms with [tex]\(x\)[/tex]: [tex]\(6x\)[/tex] and [tex]\(-5x\)[/tex]
- Constant term: [tex]\(-7\)[/tex]
2. Combine the like terms:
- For [tex]\(x^3\)[/tex]:
- [tex]\(4x^3 + 3x^3 = 7x^3\)[/tex]
- For [tex]\(x^2\)[/tex]:
- Since there is no [tex]\(x^2\)[/tex] term in the first expression, we take [tex]\(-5x^2\)[/tex] from the second one, resulting in [tex]\(-5x^2\)[/tex].
- For [tex]\(x\)[/tex]:
- [tex]\(6x - 5x = x\)[/tex]
- For the constant term:
- [tex]\(-7\)[/tex] stays [tex]\(-7\)[/tex], as it's just a constant term.
3. Write the combined expression:
Putting it all together, the expression in its simplest form is:
[tex]\[
7x^3 - 5x^2 + x - 7
\][/tex]
So, the correct choice is [tex]\(7x^3 - 5x^2 + x - 7\)[/tex].
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