Let's simplify the expression step by step:
Given: \[ -(5x - 2)(4x + 8) + 3x^2 - 9x \]
First, we will expand the term \(-(5x - 2)(4x + 8)\).
Using the distributive property (FOIL method): \[ (5x - 2)(4x + 8) = 5x \cdot 4x + 5x \cdot 8 - 2 \cdot 4x - 2 \cdot 8 \] \[ = 20x^2 + 40x - 8x - 16 \] \[ = 20x^2 + 32x - 16 \]
Now, we apply the negative sign: \[ -(20x^2 + 32x - 16) = -20x^2 - 32x + 16 \]
Next, we combine this result with \(3x^2 - 9x\): \[ -20x^2 - 32x + 16 + 3x^2 - 9x \] Now, we combine like terms:
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The \(x^2\) terms: \[ -20x^2 + 3x^2 = -17x^2 \]
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The \(x\) terms: \[ -32x - 9x = -41x \]
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The constant term: \[ 16 \]
Putting it all together, we have: \[ -17x^2 - 41x + 16 \]
The final simplified expression is: \[ \boxed{-17x^2 - 41x + 16} \]
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