To simplify the expression \(- (5x - 2)(4x + 8) + 3x^2 - 9x\), we can break it down step by step.
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Distribute the first term: \[
- (5x - 2)(4x + 8) \] To perform this operation, we first need to multiply \( (5x - 2) \) and \( (4x + 8) \):
\[ (5x - 2)(4x + 8) = 5x \cdot 4x + 5x \cdot 8 - 2 \cdot 4x - 2 \cdot 8 \] \[ = 20x^2 + 40x - 8x - 16 \] \[ = 20x^2 + 32x - 16 \]
Applying the negative sign: \[
- (20x^2 + 32x - 16) = -20x^2 - 32x + 16 \]
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Combine the rest of the expression: Now we have: \[ -20x^2 - 32x + 16 + 3x^2 - 9x \]
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Combine like terms: Combine the \(x^2\) terms: \[ -20x^2 + 3x^2 = -17x^2 \]
Combine the \(x\) terms: \[ -32x - 9x = -41x \]
The constant term remains: \[
- 16 \]
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Final expression: Putting it all together, we get: \[ -17x^2 - 41x + 16 \]
Thus, the simplified form of the expression is: \[ \boxed{-17x^2 - 41x + 16} \]
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