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 \( 2r^2 + 3r + 6 \), you can combine like terms:

1. Combine the \( r^2 \) terms: \[ 2r^2 + 2r^2 = 4r^2 \]

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

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

Putting it all together, the sum of the two polynomials is: \[ 4r^2 + 0r + 10 \]

Since \( 0r \) is essentially zero, we can simplify this to: \[ 4r^2 + 10 \]

So, the final result is: \[ \boxed{4r^2 + 10} \]