Sameeksha had Rs `(58x^(2) + 6x - 3)` with her. She spent Rs ` (19x^(2) - 2x -1)` out of it. What amount (in Rs) is left with her?

Options

A. `45x^(2) + 4x -2`
B. `39x^(2) + 8x -2`
C. `77x^(2) + 4x -4`
D. `39 x^(2) + 4x -2`

Answer

To find out how much money Sameeksha has left after her spending, we will subtract the amount she spent from the amount she initially had.

### Step-by-Step Solution:

1. **Identify the initial amount and the amount spent:**
- Initial amount: \( 58x^2 + 6x - 3 \)
- Amount spent: \( 19x^2 - 2x - 1 \)

2. **Set up the equation for the remaining amount:**
- Remaining amount = Initial amount - Amount spent
- This can be expressed as:
\[ \text{Remaining amount} = (58x^2 + 6x - 3) - (19x^2 - 2x - 1) \]

3. **Distribute the negative sign:**
- When subtracting the second expression, distribute the negative sign:
\[ \text{Remaining amount} = 58x^2 + 6x - 3 - 19x^2 + 2x + 1 \]

4. **Combine like terms:**
- Combine the \(x^2\) terms:
\[ 58x^2 - 19x^2 = 39x^2 \]
- Combine the \(x\) terms:
\[ 6x + 2x = 8x \]
- Combine the constant terms:
\[ -3 + 1 = -2 \]

5. **Write the final expression for the remaining amount:**
- Putting it all together, we have:
\[ \text{Remaining amount} = 39x^2 + 8x - 2 \]

### Final Answer:
The amount left with Sameeksha is \( 39x^2 + 8x - 2 \) Rs.