Sure, let's work through the simplification step-by-step for the given algebraic expression:
[tex]\[
2(x - 1) + 3x - x(x + 2)
\][/tex]
### Step 1: Distribute the constants and simplify the terms within each grouping
1. Distribute the 2 in [tex]\(2(x - 1)\)[/tex]:
[tex]\[
2(x - 1) = 2x - 2
\][/tex]
2. Next, we have a simple term [tex]\(3x\)[/tex].
3. Distribute the [tex]\(x\)[/tex] in [tex]\( -x(x + 2) \)[/tex]:
[tex]\[
-x(x + 2) = -x^2 - 2x
\][/tex]
So, after distributing, we have:
[tex]\[
2x - 2 + 3x - x^2 - 2x
\][/tex]
### Step 2: Combine like terms
1. Combine the [tex]\(x\)[/tex]-terms:
[tex]\[
2x + 3x - 2x = 3x
\][/tex]
Therefore, our expression now simplifies to:
[tex]\[
3x - 2 - x^2
\][/tex]
### Step 3: Arrange the polynomial in descending order (if desired)
It is standard practice to write polynomial expressions with the highest power first:
[tex]\[
-x^2 + 3x - 2
\][/tex]
Thus, the simplified form of the given expression is:
[tex]\[
-x^2 + 3x - 2
\][/tex]
This completes our simplification process.
