Answer :
To simplify the expression [tex]\((4x^3 - 3x - 7) + (3x^3 + 5x + 3)\)[/tex], follow these steps:
1. Identify Like Terms: First, recognize the like terms in the polynomials:
- The cubic terms: [tex]\(4x^3\)[/tex] and [tex]\(3x^3\)[/tex].
- The linear terms: [tex]\(-3x\)[/tex] and [tex]\(5x\)[/tex].
- The constant terms: [tex]\(-7\)[/tex] and [tex]\(3\)[/tex].
2. Add Like Terms Together:
- For the cubic terms:
[tex]\[
4x^3 + 3x^3 = 7x^3
\][/tex]
- For the linear terms:
[tex]\[
-3x + 5x = 2x
\][/tex]
- For the constant terms:
[tex]\[
-7 + 3 = -4
\][/tex]
3. Combine the Terms into a Single Polynomial:
- Combine the results from each set of like terms:
[tex]\[
7x^3 + 2x - 4
\][/tex]
Thus, the simplified expression is [tex]\(7x^3 + 2x - 4\)[/tex].
Therefore, the correct simplification from the given options is [tex]\(7x^3 + 2x - 4\)[/tex].
1. Identify Like Terms: First, recognize the like terms in the polynomials:
- The cubic terms: [tex]\(4x^3\)[/tex] and [tex]\(3x^3\)[/tex].
- The linear terms: [tex]\(-3x\)[/tex] and [tex]\(5x\)[/tex].
- The constant terms: [tex]\(-7\)[/tex] and [tex]\(3\)[/tex].
2. Add Like Terms Together:
- For the cubic terms:
[tex]\[
4x^3 + 3x^3 = 7x^3
\][/tex]
- For the linear terms:
[tex]\[
-3x + 5x = 2x
\][/tex]
- For the constant terms:
[tex]\[
-7 + 3 = -4
\][/tex]
3. Combine the Terms into a Single Polynomial:
- Combine the results from each set of like terms:
[tex]\[
7x^3 + 2x - 4
\][/tex]
Thus, the simplified expression is [tex]\(7x^3 + 2x - 4\)[/tex].
Therefore, the correct simplification from the given options is [tex]\(7x^3 + 2x - 4\)[/tex].
