Certainly! Let's simplify the given expression step by step.
Given the expression [tex]\((2x + 3)(x - 4)\)[/tex]:
1. Apply the Distributive Property (FOIL Method):
[tex]\[
(2x + 3)(x - 4) = 2x(x) + 2x(-4) + 3(x) + 3(-4)
\][/tex]
2. Multiply each term:
[tex]\[
= 2x^2 - 8x + 3x - 12
\][/tex]
3. Combine like terms:
[tex]\[
= 2x^2 - 8x + 3x - 12
= 2x^2 - 5x - 12
\][/tex]
So, the simplified expression is [tex]\(2x^2 - 5x - 12\)[/tex].
Now, let's compare this result with the options provided:
A. [tex]\(2x^2 + 5x + 12\)[/tex]
B. [tex]\(2x^2 - 5x - 12\)[/tex]
C. [tex]\(2x^2 - 5x + 12\)[/tex]
D. [tex]\(2x^2 + 5x - 12\)[/tex]
The correct answer is option B: [tex]\(2x^2 - 5x - 12\)[/tex].
