Question

Perform the operation(s) and simplify completely.

−(5x3+7x−8)+(3x−5)(−x2+7x+2)

Answer 1

To simplify the given expression \(- (5x^3 + 7x - 8) + (3x - 5)(-x^2 + 7x + 2)\), we will first simplify each part separately and then combine the results.

### Step 1: Distributing the negative sign

Starting with the first part:

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

### Step 2: Simplifying the second part

Next, we simplify the second part \((3x - 5)(-x^2 + 7x + 2)\) by using the distributive property (also known as the FOIL method for binomials):

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

Calculating each term:

1. \(3x \cdot -x^2 = -3x^3\)
2. \(3x \cdot 7x = 21x^2\)
3. \(3x \cdot 2 = 6x\)
4. \(-5 \cdot -x^2 = 5x^2\)
5. \(-5 \cdot 7x = -35x\)
6. \(-5 \cdot 2 = -10\)

Now, we combine these results:

\[
-3x^3 + 21x^2 + 6x + 5x^2 - 35x - 10
\]

Combining like terms:

1. The \(x^3\) term: \(-3x^3\)
2. The \(x^2\) terms: \(21x^2 + 5x^2 = 26x^2\)
3. The \(x\) terms: \(6x - 35x = -29x\)
4. The constant term: \(-10\)

Thus, we have:

\[
-3x^3 + 26x^2 - 29x - 10
\]

### Step 3: Combining both parts

Now we combine the results of both steps:

\[
-5x^3 - 7x + 8 + (-3x^3 + 26x^2 - 29x - 10)
\]

Combining like terms:

1. The \(x^3\) terms: \(-5x^3 - 3x^3 = -8x^3\)
2. The \(x^2\) term: \(26x^2\)
3. The \(x\) terms: \(-7x - 29x = -36x\)
4. The constant terms: \(8 - 10 = -2\)

### Final expression

Combining all of these together gives us the final simplified expression:

\[
-8x^3 + 26x^2 - 36x - 2
\]

Thus, the complete simplification of the expression is:

\[
\boxed{-8x^3 + 26x^2 - 36x - 2}
\]