Question

16 Which expression is equivalent to (10 + 7r - r ^ 2) + (- 6r ^ 2 - 18 + 5r)
Q
G 7r ^ 2 + 12r + 8
H - 7r ^ 2 + 12r - 8
F - 7r ^ 2 + 2r + 8
7r ^ 2 + 2r - 8

Answer 1

To simplify the expression \((10 + 7r - r^2) + (-6r^2 - 18 + 5r)\), we can first combine like terms step by step.

1. Rewrite the expression:
\[
10 + 7r - r^2 - 6r^2 - 18 + 5r
\]

2. Group the like terms together:
- Constant terms: \(10 - 18\)
- \(r\) terms: \(7r + 5r\)
- \(r^2\) terms: \(-r^2 - 6r^2\)

3. Combine the constant terms:
\[
10 - 18 = -8
\]

4. Combine the \(r\) terms:
\[
7r + 5r = 12r
\]

5. Combine the \(r^2\) terms:
\[
-r^2 - 6r^2 = -7r^2
\]

6. Putting it all together, we have:
\[
-7r^2 + 12r - 8
\]

Thus, the expression simplifies to:

\[
\boxed{-7r^2 + 12r - 8}
\]

This matches answer choice \(H\).