Simplify: [tex]$-x^3 + 5x + 7x^2 + 8x^3 - \left(-x^3 + x\right)$[/tex]

A. [tex][tex]$8x^3 + 7x^2 + 4x$[/tex][/tex]

B. [tex]$8x^3 + 11x^2 + 4x$[/tex]

C. [tex]$8x^3 + 11x^2 + 7x$[/tex]

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



Answer :

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]