Answer:
The correct answer is option b) −17x^2 − 41x + 16.
Explanation:
1. Start by distributing the negative sign to both terms inside the parentheses:
−(5x−2)(4x+8) = −5x(4x+8) + 2(4x+8)
2. Multiply each term inside the parentheses by the term outside the parentheses:
−5x(4x+8) + 2(4x+8) = −20x^2 − 40x + 8x + 16
3. Combine like terms:
−20x^2 − 40x + 8x + 16 = −20x^2 − 32x + 16
4. Now, add the remaining terms:
−20x^2 − 32x + 16 + 3x^2 − 9x = −20x^2 + 3x^2 − 32x − 9x + 16
5. Combine like terms again:
−20x^2 + 3x^2 − 32x − 9x + 16 = −17x^2 − 41x + 16
Therefore, the simplified form of the expression is:
−17x^2 − 41x + 16