Answer :
We start with the expression
[tex]$$
\left(4x^3 - 5x\right) + \left(8x - 3x^3\right).
$$[/tex]
Step 1: Group like terms.
Group the terms with [tex]$x^3$[/tex] together and the terms with [tex]$x$[/tex] together:
[tex]$$
(4x^3 - 3x^3) + (-5x + 8x).
$$[/tex]
Step 2: Simplify each group.
For the [tex]$x^3$[/tex] terms:
[tex]$$
4x^3 - 3x^3 = (4 - 3)x^3 = 1x^3 = x^3.
$$[/tex]
For the [tex]$x$[/tex] terms:
[tex]$$
-5x + 8x = (-5 + 8)x = 3x.
$$[/tex]
Step 3: Write the final simplified expression.
Combine the simplified groups:
[tex]$$
x^3 + 3x.
$$[/tex]
This simplified expression corresponds to option (A).
Thus, the answer is option (A):
[tex]$$
\boxed{x^3 + 3x}.
$$[/tex]
[tex]$$
\left(4x^3 - 5x\right) + \left(8x - 3x^3\right).
$$[/tex]
Step 1: Group like terms.
Group the terms with [tex]$x^3$[/tex] together and the terms with [tex]$x$[/tex] together:
[tex]$$
(4x^3 - 3x^3) + (-5x + 8x).
$$[/tex]
Step 2: Simplify each group.
For the [tex]$x^3$[/tex] terms:
[tex]$$
4x^3 - 3x^3 = (4 - 3)x^3 = 1x^3 = x^3.
$$[/tex]
For the [tex]$x$[/tex] terms:
[tex]$$
-5x + 8x = (-5 + 8)x = 3x.
$$[/tex]
Step 3: Write the final simplified expression.
Combine the simplified groups:
[tex]$$
x^3 + 3x.
$$[/tex]
This simplified expression corresponds to option (A).
Thus, the answer is option (A):
[tex]$$
\boxed{x^3 + 3x}.
$$[/tex]
