Question

Subtract the sum of x squared minus 6 x plus 10 and 7 x squared plus 11 x plus 4 from the sum of 9 x squared minus 5 x plus 8 and negative x squared plus 4 x plus 10.

Answer 1

Let's break this down step by step.

First, we need to find the sum of \(9x^2 - 5x + 8\) and \(-x^2 + 4x + 10\).

1. **Finding the first sum:**
\[
(9x^2 - 5x + 8) + (-x^2 + 4x + 10)
\]
Combine like terms:
\[
(9x^2 - x^2) + (-5x + 4x) + (8 + 10) = 8x^2 - x + 18
\]

Next, we need to find the sum of \(x^2 - 6x + 10\) and \(7x^2 + 11x + 4\).

2. **Finding the second sum:**
\[
(x^2 - 6x + 10) + (7x^2 + 11x + 4)
\]
Combine like terms:
\[
(x^2 + 7x^2) + (-6x + 11x) + (10 + 4) = 8x^2 + 5x + 14
\]

Now, we need to subtract the second sum from the first sum:
\[
(8x^2 - x + 18) - (8x^2 + 5x + 14)
\]
Distributing the negative:
\[
8x^2 - x + 18 - 8x^2 - 5x - 14
\]
Combine like terms:
\[
(8x^2 - 8x^2) + (-x - 5x) + (18 - 14) = 0 - 6x + 4 = -6x + 4
\]

Thus, the final answer is:
\[
\boxed{-6x + 4}
\]