To simplify the expression \((5x-2)(4x+8)+3x^2-9x\), we'll first expand the product \((5x-2)(4x+8)\) and then combine like terms.
- Expand \((5x-2)(4x+8)\):
\[ (5x)(4x) + (5x)(8) + (-2)(4x) + (-2)(8) \] \[ = 20x^2 + 40x - 8x - 16 \] \[ = 20x^2 + (40x - 8x) - 16 \] \[ = 20x^2 + 32x - 16 \]
- Now, add \(3x^2 - 9x\):
We combine this with the expanded form:
\[ 20x^2 + 32x - 16 + 3x^2 - 9x \]
- Combine like terms:
- Combine \(20x^2\) and \(3x^2\):
\[ 20x^2 + 3x^2 = 23x^2 \]
- Combine \(32x\) and \(-9x\):
\[ 32x - 9x = 23x \]
So the expression becomes:
\[ 23x^2 + 23x - 16 \]
Thus, the simplified expression is:
\[ \boxed{23x^2 + 23x - 16} \]