Answer :
To solve the expression [tex]\((3x^4 + 2 - 2x^3) + (4x^3 + 4x^4)\)[/tex], we need to combine like terms. Here's a step-by-step approach:
1. Identify Like Terms:
- Like terms are those terms that have the same variable raised to the same power. In this case, we have terms with [tex]\(x^4\)[/tex] and [tex]\(x^3\)[/tex], along with a constant.
2. Combine [tex]\(x^4\)[/tex] Terms:
- From the expression, the [tex]\(x^4\)[/tex] terms are [tex]\(3x^4\)[/tex] and [tex]\(4x^4\)[/tex].
- Combine them:
[tex]\[
3x^4 + 4x^4 = 7x^4
\][/tex]
3. Combine [tex]\(x^3\)[/tex] Terms:
- The [tex]\(x^3\)[/tex] terms are [tex]\(-2x^3\)[/tex] and [tex]\(4x^3\)[/tex].
- Combine them:
[tex]\[
-2x^3 + 4x^3 = 2x^3
\][/tex]
4. Identify Constant Term:
- There is only one constant term, which is [tex]\(+2\)[/tex].
- This remains as it is.
5. Write the Simplified Expression:
- Combine the results of the like terms to get the final simplified expression:
[tex]\[
7x^4 + 2x^3 + 2
\][/tex]
So, the correct simplified expression is [tex]\(7x^4 + 2x^3 + 2\)[/tex].
Based on these steps, the answer is A. [tex]\(7x^4 + 2x^3 + 2\)[/tex].
1. Identify Like Terms:
- Like terms are those terms that have the same variable raised to the same power. In this case, we have terms with [tex]\(x^4\)[/tex] and [tex]\(x^3\)[/tex], along with a constant.
2. Combine [tex]\(x^4\)[/tex] Terms:
- From the expression, the [tex]\(x^4\)[/tex] terms are [tex]\(3x^4\)[/tex] and [tex]\(4x^4\)[/tex].
- Combine them:
[tex]\[
3x^4 + 4x^4 = 7x^4
\][/tex]
3. Combine [tex]\(x^3\)[/tex] Terms:
- The [tex]\(x^3\)[/tex] terms are [tex]\(-2x^3\)[/tex] and [tex]\(4x^3\)[/tex].
- Combine them:
[tex]\[
-2x^3 + 4x^3 = 2x^3
\][/tex]
4. Identify Constant Term:
- There is only one constant term, which is [tex]\(+2\)[/tex].
- This remains as it is.
5. Write the Simplified Expression:
- Combine the results of the like terms to get the final simplified expression:
[tex]\[
7x^4 + 2x^3 + 2
\][/tex]
So, the correct simplified expression is [tex]\(7x^4 + 2x^3 + 2\)[/tex].
Based on these steps, the answer is A. [tex]\(7x^4 + 2x^3 + 2\)[/tex].
