Which of the following is equivalent to `2(x^2 -x)+3(x^2 -x)` ?

Options

A. `5x^2-5x`
B. `5x^2 + 5x`
C. 5x
D. `5x^2`

Explanation

To solve the expression \(2(x^2 - x) + 3(x^2 - x)\), we will follow these steps:

### Step 1: Distribute the constants
We start by distributing the constants \(2\) and \(3\) to the expression \(x^2 - x\).

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

### Step 2: Combine the results
Now, we combine the results from Step 1.

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

### Step 3: Combine like terms
Next, we combine the like terms. The like terms are \(2x^2\) and \(3x^2\), and \(-2x\) and \(-3x\).

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

### Final Result
Thus, the expression \(2(x^2 - x) + 3(x^2 - x)\) simplifies to:

\[ 5x^2 - 5x \]

### Conclusion
The equivalent expression is \(5x^2 - 5x\).

---