Let's simplify the expression step by step:
Given:
\[ (5e^2 - 6e + 7) - (4e^2 - 6e - 2) \]
First, distribute the negative sign in front of the second parentheses:
\[ 5e^2 - 6e + 7 - 4e^2 + 6e + 2 \]
Now, combine like terms. Start with the \(e^2\) terms:
\[ 5e^2 - 4e^2 = e^2 \]
Next, combine the \(e\) terms:
\[ -6e + 6e = 0 \]
Now combine the constant terms:
\[ 7 + 2 = 9 \]
Putting it all together, we have:
\[ e^2 + 9 \]
So, the simplified expression is:
\[ e^2 + 9 \]
The correct response is:
e^2 + 9