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------------------------------------------------ What is [tex]\left(3x^4 + 2 - 2x^3\right) + \left(4x^3 + 4x^4\right)[/tex]?

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

Sure! Let's simplify the expression [tex]\((3x^4 + 2 - 2x^3) + (4x^3 + 4x^4)\)[/tex] by combining like terms.

1. Identify like terms:
- Terms with [tex]\(x^4\)[/tex]: [tex]\(3x^4\)[/tex] and [tex]\(4x^4\)[/tex]
- Terms with [tex]\(x^3\)[/tex]: [tex]\(-2x^3\)[/tex] and [tex]\(4x^3\)[/tex]
- Constant term: [tex]\(2\)[/tex]

2. Combine the like terms:
- For [tex]\(x^4\)[/tex] terms: [tex]\(3x^4 + 4x^4 = 7x^4\)[/tex]
- For [tex]\(x^3\)[/tex] terms: [tex]\(-2x^3 + 4x^3 = 2x^3\)[/tex]
- The constant term remains as: [tex]\(+2\)[/tex]

3. Write the simplified expression:
- Combining all the terms gives us [tex]\(7x^4 + 2x^3 + 2\)[/tex]

Therefore, the simplified expression is [tex]\(7x^4 + 2x^3 + 2\)[/tex].

Comparing this with the given options, the correct answer is:

(1) [tex]\(7x^4 + 2x^3 + 2\)[/tex]