perform the operation(s) and simplify completely. −(5x−2)(4x+8)+3x2−9x (1 point) Responses −17x2−41x+16 negative 17 x squared minus 41 x plus 16 −17x2+23x−16 negative 17 x squared plus 23 x minus 16 23x2+23x−16 23 x squared plus 23 x minus 16 3x2+10

Answer 1

To simplify the expression \(- (5x - 2)(4x + 8) + 3x^2 - 9x\), we will follow these steps:

1. Expand the product: \[

   • (5x - 2)(4x + 8) \] First, we need to expand \((5x - 2)(4x + 8)\): \[ = 5x \cdot 4x + 5x \cdot 8 - 2 \cdot 4x - 2 \cdot 8 \] \[ = 20x^2 + 40x - 8x - 16 \] \[ = 20x^2 + 32x - 16 \]

   Now apply the negative: \[

   • (20x^2 + 32x - 16) = -20x^2 - 32x + 16 \]

2. Combine with the other terms: Now add \(3x^2 - 9x\): \[ -20x^2 - 32x + 16 + 3x^2 - 9x \]

3. Combine like terms: For the \(x^2\) terms: \[ -20x^2 + 3x^2 = -17x^2 \] For the \(x\) terms: \[ -32x - 9x = -41x \] The constant term remains: \[

   • 16 \]

4. Final expression: Combining all these results gives: \[ -17x^2 - 41x + 16 \]

Thus, the simplified expression is: \[ \boxed{-17x^2 - 41x + 16} \]