Question

Perform the operation(s) and simplify completely.

5(x2−4x+4)x−2+(x+1)(x2−x+3)

(1 point)
Responses

x3+x−13
x cubed plus x minus 13

x3+2x2+9x−7
x cubed plus 2 x squared plus 9 x minus 7

x3+7x+13
x cubed plus 7 x plus 13

x3+7x−7

Answer 1

Let's break down the expression step by step:

The expression you provided is:

\[ 5(x^2 - 4x + 4)x - 2 + (x + 1)(x^2 - x + 3) \]

**Step 1: Simplify \(5(x^2 - 4x + 4)x - 2\)**

First, we will distribute \(5\) and then multiply by \(x\):

\[
5(x^2 - 4x + 4)x = 5x(x^2 - 4x + 4) = 5x^3 - 20x^2 + 20x
\]

Now, subtract \(2\):

\[
5x^3 - 20x^2 + 20x - 2
\]

**Step 2: Simplify \((x + 1)(x^2 - x + 3)\)**

Now we will distribute \((x + 1)\) across \((x^2 - x + 3)\):

\[
(x + 1)(x^2 - x + 3) = x(x^2 - x + 3) + 1(x^2 - x + 3)
\]

Calculating this out gives:

\[
= x^3 - x^2 + 3x + x^2 - x + 3 = x^3 + 2x + 3
\]

**Step 3: Combine the Simplified Parts**

Now combine everything:

\[
5x^3 - 20x^2 + 20x - 2 + x^3 + 2x + 3
\]

Combine like terms:

1. For \(x^3\): \(5x^3 + x^3 = 6x^3\)
2. For \(x^2\): \(-20x^2\)
3. For \(x\): \(20x + 2x = 22x\)
4. For the constant: \(-2 + 3 = 1\)

Putting it all together:

\[
6x^3 - 20x^2 + 22x + 1
\]

Now let's look at the original provided options again. None of these options match (as we simplified to \(6x^3 - 20x^2 + 22x + 1\)). We reconsider possibility of scaling, or if there's an error in the options or calculations.

Final expression in ordered polynomial form would be:

\[
6x^3 - 20x^2 + 22x + 1
\]

Which still does not appear in the responses given. Could you please double-check the math and clarify if that was the intended problem?