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Answer :
To solve the expression [tex]\((3x^4 + 2 - 2x^3) + (4x^3 + 4x^4)\)[/tex], we need to combine like terms.
Step-by-step solution:
1. Identify Like Terms:
- Terms with the same variable and exponent are called like terms.
- Here, we have terms with [tex]\(x^4\)[/tex], terms with [tex]\(x^3\)[/tex], and a constant term.
2. Combine [tex]\(x^4\)[/tex] Terms:
- Look at the [tex]\(x^4\)[/tex] terms: [tex]\(3x^4\)[/tex] from the first expression and [tex]\(4x^4\)[/tex] from the second expression.
- Add them together: [tex]\(3x^4 + 4x^4 = 7x^4\)[/tex].
3. Combine [tex]\(x^3\)[/tex] Terms:
- Look at the [tex]\(x^3\)[/tex] terms: [tex]\(-2x^3\)[/tex] from the first expression and [tex]\(4x^3\)[/tex] from the second expression.
- Add them together: [tex]\(-2x^3 + 4x^3 = 2x^3\)[/tex].
4. Combine Constant Terms:
- The only constant term is [tex]\(+2\)[/tex], which remains the same since there are no other constant terms to combine.
5. Write the Final Expression:
- After combining like terms, the resulting expression is [tex]\(7x^4 + 2x^3 + 2\)[/tex].
Therefore, the correct answer is [tex]\(\boxed{C. \, 7x^4 + 7x^3 + 2}\)[/tex].
Step-by-step solution:
1. Identify Like Terms:
- Terms with the same variable and exponent are called like terms.
- Here, we have terms with [tex]\(x^4\)[/tex], terms with [tex]\(x^3\)[/tex], and a constant term.
2. Combine [tex]\(x^4\)[/tex] Terms:
- Look at the [tex]\(x^4\)[/tex] terms: [tex]\(3x^4\)[/tex] from the first expression and [tex]\(4x^4\)[/tex] from the second expression.
- Add them together: [tex]\(3x^4 + 4x^4 = 7x^4\)[/tex].
3. Combine [tex]\(x^3\)[/tex] Terms:
- Look at the [tex]\(x^3\)[/tex] terms: [tex]\(-2x^3\)[/tex] from the first expression and [tex]\(4x^3\)[/tex] from the second expression.
- Add them together: [tex]\(-2x^3 + 4x^3 = 2x^3\)[/tex].
4. Combine Constant Terms:
- The only constant term is [tex]\(+2\)[/tex], which remains the same since there are no other constant terms to combine.
5. Write the Final Expression:
- After combining like terms, the resulting expression is [tex]\(7x^4 + 2x^3 + 2\)[/tex].
Therefore, the correct answer is [tex]\(\boxed{C. \, 7x^4 + 7x^3 + 2}\)[/tex].
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