College

Simplify the expression:

[tex]\left(3x^3 + 2x^2 + 4x\right) + \left(4x^3 + 6x^2 - 3x\right)[/tex]

A. [tex]7x^3 + 8x^2 + x[/tex]

B. [tex]7x^3 + 4x^2 + x[/tex]

C. [tex]7x^3 + 8x^2 - x[/tex]

D. [tex]7x^3 + 4x^2 - x[/tex]

Answer :

To simplify the expression [tex]\((3x^3 + 2x^2 + 4x) + (4x^3 + 6x^2 - 3x)\)[/tex], we will combine like terms. Here’s how you do it step-by-step:

1. Identify Like Terms:
- The first set of like terms is [tex]\(x^3\)[/tex]: [tex]\(3x^3\)[/tex] from the first expression and [tex]\(4x^3\)[/tex] from the second expression.
- The next set is [tex]\(x^2\)[/tex]: [tex]\(2x^2\)[/tex] from the first expression and [tex]\(6x^2\)[/tex] from the second expression.
- The last set is [tex]\(x\)[/tex]: [tex]\(4x\)[/tex] from the first expression and [tex]\(-3x\)[/tex] from the second expression.

2. Combine Like Terms:
- For [tex]\(x^3\)[/tex] terms: [tex]\(3x^3 + 4x^3 = 7x^3\)[/tex].
- For [tex]\(x^2\)[/tex] terms: [tex]\(2x^2 + 6x^2 = 8x^2\)[/tex].
- For [tex]\(x\)[/tex] terms: [tex]\(4x - 3x = 1x\)[/tex].

3. Write the Simplified Expression:
- Combine all the simplified like terms together: [tex]\(7x^3 + 8x^2 + 1x\)[/tex].

So the simplified form of the given expression is [tex]\(7x^3 + 8x^2 + x\)[/tex].

This matches with option A: [tex]\(7x^3 + 8x^2 + x\)[/tex].