Let's simplify the expression step by step:
Given: \[ -(2x + 6)(3x + 4) + 5x^2 - 7x \] First, we'll start by expanding the product \(-(2x + 6)(3x + 4)\).
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Expand \((2x + 6)(3x + 4)\): \[ (2x)(3x) + (2x)(4) + (6)(3x) + (6)(4) = 6x^2 + 8x + 18x + 24 = 6x^2 + 26x + 24 \]
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Now, applying the negative sign: \[ -(6x^2 + 26x + 24) = -6x^2 - 26x - 24 \]
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Now, we substitute this back into the original expression: \[ -6x^2 - 26x - 24 + 5x^2 - 7x \]
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Combine like terms:
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For \(x^2\) terms: \[-6x^2 + 5x^2 = -x^2\]
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For \(x\) terms: \[-26x - 7x = -33x\]
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For constant terms: \[-24\] (there are no other constants to combine with).
Thus, we get: \[ -x^2 - 33x - 24 \]
The simplified expression is: \[ -x^2 - 33x - 24 \]
So the answer is: −x²−33x−24 (negative x squared minus 33 x minus 24).