Question

Which expression is equivalent to 3x^2 + (5x-7x^2) + 8 - (4x+5) ?

19x+ 3

-4x^2 + x + 3

-4x^2 + 9x - 3

-3x - 3

Answer 1

To simplify the expression \(3x^2 + (5x - 7x^2) + 8 - (4x + 5)\), we can follow these steps:

1. Distribute the negative sign in \(-(4x + 5)\):
\[
-4x - 5
\]

2. Substitute back into the expression:
\[
3x^2 + (5x - 7x^2) + 8 - 4x - 5
\]

3. Now, combine the terms inside the parentheses:
\[
5x - 7x^2
\]
So we can write:
\[
3x^2 - 7x^2 + 5x - 4x + 8 - 5
\]

4. Combine like terms:
- For the \(x^2\) terms:
\[
3x^2 - 7x^2 = -4x^2
\]
- For the \(x\) terms:
\[
5x - 4x = 1x = x
\]
- For the constant terms:
\[
8 - 5 = 3
\]

5. Putting it all together, we have:
\[
-4x^2 + x + 3
\]

So the expression simplified is \(-4x^2 + x + 3\).

Thus, the equivalent expression is:
\[
\boxed{-4x^2 + x + 3}
\]