Let's simplify the expression \(- (5x - 2)(4x + 8) + 3x^2 - 9x\) step by step.
- Distribute: Start by expanding \(-(5x - 2)(4x + 8)\).
\[ (5x - 2)(4x + 8) = 5x(4x) + 5x(8) - 2(4x) - 2(8) \]
Calculating each term:
- \(5x \cdot 4x = 20x^2\)
- \(5x \cdot 8 = 40x\)
- \(-2 \cdot 4x = -8x\)
- \(-2 \cdot 8 = -16\)
Now combine all those terms:
\[ (5x - 2)(4x + 8) = 20x^2 + 40x - 8x - 16 = 20x^2 + 32x - 16 \]
Now apply the negative sign:
\[ -(20x^2 + 32x - 16) = -20x^2 - 32x + 16 \]
- Combine with the other terms: Now substitute this back into the original expression:
\[ -20x^2 - 32x + 16 + 3x^2 - 9x \]
Next, combine like terms:
- Combine \( -20x^2 + 3x^2 \):
\[ -20x^2 + 3x^2 = -17x^2 \]
- Combine \( -32x - 9x \):
\[ -32x - 9x = -41x \]
So now, we have:
\[ -17x^2 - 41x + 16 \]
- Final answer: The simplified expression is:
\[ \boxed{-17x^2 - 41x + 16} \]