Simplify the expression (5e2−6e+7)−(4e2−6e−2) .(1 point) Responses e2−12e+9 e squared minus 12 e plus 9 9e2+9 9 e squared plus 9 9e2−12e+5 9 e squared minus 12 e plus 5 e2+9

Answer 1

To simplify the expression \((5e^2 - 6e + 7) - (4e^2 - 6e - 2)\), first distribute the negative sign across the second polynomial:

\[ (5e^2 - 6e + 7) - (4e^2 - 6e - 2) = 5e^2 - 6e + 7 - 4e^2 + 6e + 2 \]

Now, combine like terms:

1. For \(e^2\) terms: \(5e^2 - 4e^2 = 1e^2\)
2. For \(e\) terms: \(-6e + 6e = 0\)
3. For constant terms: \(7 + 2 = 9\)

Putting it all together:

\[ 1e^2 + 0e + 9 = e^2 + 9 \]

So, the simplified expression is:

\[ e^2 + 9 \]

Thus, the correct answer from the provided options is \(e^2 + 9\).