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------------------------------------------------ Simplify [tex]5x^7 + 7x^3 + 4x^7 + 2 + 6x^3[/tex].

A. [tex]9x^7 + 13x^3 + 2[/tex]
B. [tex]20x^7 + 42x^3 + 1[/tex]
C. [tex]9x^{14} + 13x^3 + 2[/tex]

Answer :

To simplify the expression [tex]\(5x^7 + 7x^3 + 4x^7 + 2 + 6x^3\)[/tex], you need to combine like terms. Here's how you can do it step-by-step:

1. Identify Like Terms:
- Terms with [tex]\(x^7\)[/tex]: [tex]\(5x^7\)[/tex] and [tex]\(4x^7\)[/tex].
- Terms with [tex]\(x^3\)[/tex]: [tex]\(7x^3\)[/tex] and [tex]\(6x^3\)[/tex].
- Constant term: [tex]\(2\)[/tex].

2. Combine Like Terms:
- For the [tex]\(x^7\)[/tex] terms: Combine [tex]\(5x^7\)[/tex] and [tex]\(4x^7\)[/tex].
- [tex]\(5x^7 + 4x^7 = 9x^7\)[/tex].
- For the [tex]\(x^3\)[/tex] terms: Combine [tex]\(7x^3\)[/tex] and [tex]\(6x^3\)[/tex].
- [tex]\(7x^3 + 6x^3 = 13x^3\)[/tex].
- The constant [tex]\(2\)[/tex] remains as it is.

3. Write the Simplified Expression:
- After combining the like terms, the simplified expression is:

[tex]\[
9x^7 + 13x^3 + 2
\][/tex]

This is your final, simplified expression.