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------------------------------------------------ What is the simplest form of [tex]\left(4x^3 + 6x - 7\right) + \left(3x^3 - 5x^2 - 5x\right)[/tex]?

A. [tex]7x^3 - 5x^2 - x - 7[/tex]
B. [tex]7x^3 - 5x^2 + x - 7[/tex]
C. [tex]7x^3 + x^2 - 5x - 7[/tex]
D. [tex]7x^6 - 4x^2 - 7[/tex]

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].