Let's break down the expression step by step:
The expression is: \[ -(2x + 6)(3x + 4) + 5x^2 - 7x \]
Step 1: Distributing the first part
First, we will simplify \(-(2x + 6)(3x + 4)\).
Using the distributive property (FOIL): \[ (2x + 6)(3x + 4) = 2x \cdot 3x + 2x \cdot 4 + 6 \cdot 3x + 6 \cdot 4 \] \[ = 6x^2 + 8x + 18x + 24 \] \[ = 6x^2 + 26x + 24 \]
Now we apply the negative sign: \[ -(6x^2 + 26x + 24) = -6x^2 - 26x - 24 \]
Step 2: Combine it with the other terms
Now let's add \(5x^2 - 7x\): \[ -6x^2 - 26x - 24 + 5x^2 - 7x \]
Step 3: Combine like terms
- For the \(x^2\) terms: \(-6x^2 + 5x^2 = -1x^2\)
- For the \(x\) terms: \(-26x - 7x = -33x\)
- The constant term remains: \(-24\)
Putting it all together: \[ -x^2 - 33x - 24 \]
Final Result:
The simplified expression is: \[ \boxed{-x^2 - 33x - 24} \]
Therefore, the correct response is: −x²−33x−24 (negative x squared minus 33 x minus 24).