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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.
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.
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