Question

Find each difference.
(2x^2 + 2x+3) -(x^2 +2x+1) = choose your answer...

Answer 1

To find the difference between the two polynomials \((2x^2 + 2x + 3) - (x^2 + 2x + 1)\), we can follow these steps:

1. Distribute the negative sign across the second polynomial:
\[
(2x^2 + 2x + 3) - (x^2 + 2x + 1) = 2x^2 + 2x + 3 - x^2 - 2x - 1
\]

2. Combine like terms:
- For \(x^2\) terms: \(2x^2 - x^2 = x^2\)
- For \(x\) terms: \(2x - 2x = 0\)
- For constant terms: \(3 - 1 = 2\)

3. Combining all the results, we have:
\[
x^2 + 0 + 2 = x^2 + 2
\]

The final result is:
\[
\boxed{x^2 + 2}
\]