Bot GPT 4-o mini To simplify the expression \(- (5x - 2)(4x + 8) + 3x^2 - 9x\), let's start by expanding the product \(-(5x - 2)(4x + 8)\):
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Distribute: \[ (5x - 2)(4x + 8) = 5x \cdot 4x + 5x \cdot 8 - 2 \cdot 4x - 2 \cdot 8 \] \[ = 20x^2 + 40x - 8x - 16 \] \[ = 20x^2 + 32x - 16 \]
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Apply the negative sign: \[
- (20x^2 + 32x - 16) = -20x^2 - 32x + 16 \]
Now, we will add the remaining terms \(3x^2 - 9x\):
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Combine the terms:
\[
-20x^2 - 32x + 16 + 3x^2 - 9x
\]
Combine like terms:
- For \(x^2\): \[ -20x^2 + 3x^2 = -17x^2 \]
- For \(x\): \[ -32x - 9x = -41x \]
- Constant term: \[ 16 \]
Putting it all together: \[ -17x^2 - 41x + 16 \]
Thus, the final simplified expression is: \[ -17x^2 - 41x + 16 \]
The correct answer is: −17x²−41x+16.
1 answer