Add the polynomial expressions 2r^2 - 3r + 4 and -2r^2 + 3r + 6

Answer 1

To add the polynomial expressions \(2r^2 - 3r + 4\) and \(-2r^2 + 3r + 6\), we combine like terms.

Starting with the two polynomials:

\[ (2r^2 - 3r + 4) + (-2r^2 + 3r + 6) \]

Now we can group the like terms:

1. For the \(r^2\) terms: \[ 2r^2 + (-2r^2) = 0 \]

2. For the \(r\) terms: \[ -3r + 3r = 0 \]

3. For the constant terms: \[ 4 + 6 = 10 \]

Now, combining all these results:

\[ 0 + 0 + 10 = 10 \]

Thus, the sum of the polynomial expressions \(2r^2 - 3r + 4\) and \(-2r^2 + 3r + 6\) is:

\[ \boxed{10} \]