Which expression is equivalent to `(2x^2-4)-(-3x^2+2x-7)` ?

Options

A. `5x^2 -2x+3`
B. `5x^2 + 2x-3`
C. `-x^2 -2x-11`
D. `-x^2 + 2x-11`

Explanation

To solve the expression \( (2x^2 - 4) - (-3x^2 + 2x - 7) \), we will follow these steps:

### Step 1: Write down the expression
We start with the expression:
\[ (2x^2 - 4) - (-3x^2 + 2x - 7) \]

### Step 2: Distribute the negative sign
When we subtract the expression in the parentheses, we need to distribute the negative sign. This means that we will change the signs of all the terms inside the second parentheses:
\[ = 2x^2 - 4 + 3x^2 - 2x + 7 \]

### Step 3: Combine like terms
Now, we will combine the like terms. The like terms here are \(2x^2\) and \(3x^2\), as well as the constants \(-4\) and \(7\), and the term \(-2x\):
\[ = (2x^2 + 3x^2) + (-2x) + (-4 + 7) \]
\[ = 5x^2 - 2x + 3 \]

### Final Expression
Thus, the expression equivalent to \( (2x^2 - 4) - (-3x^2 + 2x - 7) \) is:
\[ 5x^2 - 2x + 3 \]

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