`(2-4t+5t^2)-(3t^2 + 2t -7)` is equivalent to :

Options

A. `2t^2 - 6t + 9`
B. `2t^2 -2t + 9`
C. `2t^4 - 2t^2 -5`
D. `8t^2 -6t-5`

Answer

To simplify the expression \((2 - 4t + 5t^2) - (3t^2 + 2t - 7)\), we will follow these steps:

### Step 1: Write down the expression
We start with the expression:
\[ (2 - 4t + 5t^2) - (3t^2 + 2t - 7) \]

### Step 2: Remove the brackets
When removing the brackets, we need to distribute the negative sign across the second set of parentheses:
\[ 2 - 4t + 5t^2 - 3t^2 - 2t + 7 \]

### Step 3: Combine like terms
Now we will combine the like terms. We will group the \(t^2\) terms, the \(t\) terms, and the constant terms:
- For \(t^2\) terms: \(5t^2 - 3t^2 = 2t^2\)
- For \(t\) terms: \(-4t - 2t = -6t\)
- For constant terms: \(2 + 7 = 9\)

Putting it all together, we have:
\[ 2t^2 - 6t + 9 \]

### Final Result
Thus, the simplified expression is:
\[ 2t^2 - 6t + 9 \]

### Conclusion
The expression \((2 - 4t + 5t^2) - (3t^2 + 2t - 7)\) is equivalent to \(2t^2 - 6t + 9\), which corresponds to option 1.

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