To simplify the given expression:
[tex]\[
-x^3 + 5x + 7x^2 + 8x^3 - \left(-x^3 + x\right)
\][/tex]
we need to follow a step-by-step approach:
### Step 1: Distribute the negative sign in the subexpression
First, distribute the negative sign across [tex]\(-(-x^3 + x)\)[/tex]:
[tex]\[
-(-x^3 + x) = x^3 - x
\][/tex]
So, the entire expression now is:
[tex]\[
-x^3 + 5x + 7x^2 + 8x^3 + x^3 - x
\][/tex]
### Step 2: Combine like terms
Now we group the like terms together.
#### Group [tex]\(x^3\)[/tex] terms:
[tex]\[
-x^3 + 8x^3 + x^3
\][/tex]
Combine these:
[tex]\[
(-1 + 8 + 1)x^3 = 8x^3
\][/tex]
#### Group [tex]\(x^2\)[/tex] terms:
In the expression [tex]\(7x^2\)[/tex], it remains as is because it is the only [tex]\(x^2\)[/tex] term.
[tex]\[
7x^2
\][/tex]
#### Group [tex]\(x\)[/tex] terms:
[tex]\[
5x - x
\][/tex]
Combine these:
[tex]\[
(5 - 1)x = 4x
\][/tex]
### Step 3: Write the simplified expression
Putting all the simplified terms together, we get:
[tex]\[
8x^3 + 7x^2 + 4x
\][/tex]
Therefore, the correct answer is:
A. [tex]\(8x^3 + 7x^2 + 4x\)[/tex]
