Sure, let's simplify the expression [tex]\((2x + 3)(x - 4)\)[/tex] step by step.
1. Distribute each term in the first binomial to each term in the second binomial:
[tex]\[
(2x + 3)(x - 4) = 2x \cdot x + 2x \cdot (-4) + 3 \cdot x + 3 \cdot (-4)
\][/tex]
2. Multiply the terms:
[tex]\[
2x \cdot x = 2x^2
\][/tex]
[tex]\[
2x \cdot (-4) = -8x
\][/tex]
[tex]\[
3 \cdot x = 3x
\][/tex]
[tex]\[
3 \cdot (-4) = -12
\][/tex]
3. Combine all these results together:
[tex]\[
2x^2 + (-8x) + 3x + (-12)
\][/tex]
4. Simplify by combining like terms:
[tex]\[
2x^2 + (-8x + 3x) - 12
\][/tex]
[tex]\[
= 2x^2 - 5x - 12
\][/tex]
Therefore, the simplified form of [tex]\((2x + 3)(x - 4)\)[/tex] is:
[tex]\[
2x^2 - 5x - 12
\][/tex]
The correct choice from the given options is:
A. [tex]\(2x^2 - 5x - 12\)[/tex].
