The expression to be added to `(5x^2 -7x + 2)` to produce `(7x^2 -1 )` is

Options

A. `2x^2 + 7x - 3`
B. `2x^2 +3`
C. `2x^2 - 3`
D. `2x^2 + 7x`

Answer

To find the expression that needs to be added to \(5x^2 - 7x + 2\) to produce \(7x^2 - 1\), we can set up the equation as follows:

1. **Set up the equation**:
We need to find an expression \(E\) such that:
\[ (5x^2 - 7x + 2) + E = 7x^2 - 1 \]

2. **Rearrange the equation**:
To isolate \(E\), we can rearrange the equation:
\[ E = (7x^2 - 1) - (5x^2 - 7x + 2) \]

3. **Distribute the negative sign**:
Now, distribute the negative sign across the second expression:
\[ E = 7x^2 - 1 - 5x^2 + 7x - 2 \]

4. **Combine like terms**:
Now, combine the like terms:
- Combine \(7x^2\) and \(-5x^2\):
\[ 7x^2 - 5x^2 = 2x^2 \]
- Combine the constant terms \(-1\) and \(-2\):
\[ -1 - 2 = -3 \]
- The term \(+7x\) remains as is.

Thus, we have:
\[ E = 2x^2 + 7x - 3 \]

5. **Final expression**:
Therefore, the expression that needs to be added is:
\[ \boxed{2x^2 + 7x - 3} \]