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Answer :
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]
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]
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