Question

(3x^5+7x^2−4x+8)−(4x^4+8x^2−3x+7)

Answer 1

To simplify the expression \((3x^5 + 7x^2 - 4x + 8) - (4x^4 + 8x^2 - 3x + 7)\), we need to distribute the negative sign across the second polynomial and then combine like terms.

### Step 1: Distribute the negative sign

\[
(3x^5 + 7x^2 - 4x + 8) - (4x^4 + 8x^2 - 3x + 7) = 3x^5 + 7x^2 - 4x + 8 - 4x^4 - 8x^2 + 3x - 7
\]

### Step 2: Combine like terms

Now, let's gather the like terms:

- **\(x^5\) terms**: \(3x^5\)
- **\(x^4\) terms**: \(-4x^4\)
- **\(x^2\) terms**: \(7x^2 - 8x^2 = -x^2\)
- **\(x\) terms**: \(-4x + 3x = -x\)
- **Constant terms**: \(8 - 7 = 1\)

### Step 3: Write the final expression

Now putting together all the terms we gathered:

\[
3x^5 - 4x^4 - x^2 - x + 1
\]

Therefore, the simplified expression is:

\[
\boxed{3x^5 - 4x^4 - x^2 - x + 1}
\]