Let's start with the expression:
\[ -(2x + 6)(3x + 4) + 5x^2 - 7x \]
First, we need to expand the expression \(-(2x + 6)(3x + 4)\). Let's perform the multiplication:
\[ (2x + 6)(3x + 4) = 2x \cdot 3x + 2x \cdot 4 + 6 \cdot 3x + 6 \cdot 4 \]
Calculating each term:
- \(2x \cdot 3x = 6x^2\)
- \(2x \cdot 4 = 8x\)
- \(6 \cdot 3x = 18x\)
- \(6 \cdot 4 = 24\)
Adding these together gives:
\[ 6x^2 + 8x + 18x + 24 = 6x^2 + 26x + 24 \]
Now, since we need \(-(2x + 6)(3x + 4)\), we have:
\[ -(6x^2 + 26x + 24) = -6x^2 - 26x - 24 \]
Next, we substitute back into the expression we are simplifying:
\[ -6x^2 - 26x - 24 + 5x^2 - 7x \]
Now, we combine like terms:
-
For \(x^2\) terms: \(-6x^2 + 5x^2 = -x^2\)
-
For \(x\) terms: \(-26x - 7x = -33x\)
-
The constant term remains \(-24\).
Combining everything gives:
\[ -x^2 - 33x - 24 \]
Thus, the final simplified expression is:
\[ \boxed{-x^2 - 33x - 24} \]
1 answer