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Which of the following expressions is equivalent to:

[tex]\left(4x^3 - 5x\right) + \left(8x - 3x^3\right)[/tex]?

Choose 1 answer:

A. [tex]x^3 + 3x[/tex]

B. [tex]x^3 - 3x[/tex]

C. [tex]7x^3 - 3x[/tex]

D. [tex]7x^3 + 3x[/tex]

Answer :

Sure, let's solve the given problem step-by-step.

We need to find the expression equivalent to [tex]\((4x^3 - 5x) + (8x - 3x^3)\)[/tex].

1. Distribute and Combine like terms:
- Start by re-writing the expression:
[tex]\[
(4x^3 - 5x) + (8x - 3x^3)
\][/tex]
- Open the parentheses:
[tex]\[
4x^3 - 5x + 8x - 3x^3
\][/tex]

2. Group and combine the x³ terms:
- Combine [tex]\(4x^3\)[/tex] and [tex]\(-3x^3\)[/tex]:
[tex]\[
4x^3 - 3x^3 = x^3
\][/tex]

3. Group and combine the x terms:
- Combine [tex]\(-5x\)[/tex] and [tex]\(8x\)[/tex]:
[tex]\[
-5x + 8x = 3x
\][/tex]

4. Combine all the simplified terms together:
- Adding [tex]\(x^3\)[/tex] and [tex]\(3x\)[/tex]:
[tex]\[
x^3 + 3x
\][/tex]

Therefore, the expression [tex]\((4x^3 - 5x) + (8x - 3x^3)\)[/tex] simplifies to:
[tex]\[
\boxed{x^3 + 3x}
\][/tex]

So, the correct answer is:
(A) [tex]\(x^3 + 3x\)[/tex].

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