Simplify the expression (5e2−6e+7)−(4e2−6e−2)

Question

.(1 point)
Responses

9e2−12e+5
9 e squared minus 12 e plus 5

e2−12e+9
e squared minus 12 e plus 9

e2+9
e squared plus 9

9e2+9

Answer 1

To simplify the expression \((5e^2 - 6e + 7) - (4e^2 - 6e - 2)\), we start by distributing the negative sign across the second expression:

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

Now, we will combine like terms:

1. Combine the \(e^2\) terms: \[ 5e^2 - 4e^2 = 1e^2 \]

2. Combine the \(e\) terms: \[ -6e + 6e = 0 \]

3. Combine the constant terms: \[ 7 + 2 = 9 \]

Putting it all together, we have:

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

Therefore, the simplified expression is:

\[ e^2 + 9 \]

The correct response is:

e² + 9 (e squared plus 9).