Which of the following simplifies to the same expression as 4x2−3x2+5x−24

Let's first simplify the given expression:

4x^2 − 3x^2 + 5x − 24

Combine like terms (the x^2 terms):

(4x^2 − 3x^2) + 5x − 24
x^2 + 5x − 24

Now we need to check which of the provided options simplifies to x^2 + 5x − 24.

1. 2(x−12)
This simply expands to:
2x - 24
which doesn't match our expression (it's missing the x^2 term and has a different coefficient for x).

2. 4x(x−6)
Expanding gives:
4x^2 - 24x
which doesn't match our expression either (it has the wrong coefficient for the x term and is missing the constant term).

3. (x+6)(x−4)
Expanding using the FOIL (First, Outer, Inner, Last) method gives:
x^2 - 4x + 6x - 24
Combining like terms:
x^2 + 2x - 24
This also doesn't match our expression (it has a different coefficient for the x term).

4. (x+8)(x−3)
Expanding this gives:
x^2 - 3x + 8x - 24
Combining like terms:
x^2 + 5x - 24

As you can see, the expression (x+8)(x−3) simplifies correctly to match the originally provided expression x^2 + 5x − 24. So, the correct answer is:

(x+8)(x−3)