To simplify the expression [tex]\((2x+3)(x-4)\)[/tex], we can follow these detailed steps:
1. Distribute each term in the first binomial to each term in the second binomial: Use the distributive property (also known as the FOIL method for binomials) to expand the expression.
[tex]\[
(2x + 3)(x - 4)
\][/tex]
2. Multiply the terms:
- First: Multiply the first terms of each binomial:
[tex]\[
2x \cdot x = 2x^2
\][/tex]
- Outer: Multiply the outer terms of the binomials:
[tex]\[
2x \cdot (-4) = -8x
\][/tex]
- Inner: Multiply the inner terms of the binomials:
[tex]\[
3 \cdot x = 3x
\][/tex]
- Last: Multiply the last terms of each binomial:
[tex]\[
3 \cdot (-4) = -12
\][/tex]
3. Combine all the products from the previous step:
[tex]\[
2x^2 + (-8x) + 3x + (-12)
\][/tex]
4. Combine like terms:
[tex]\[
2x^2 - 8x + 3x - 12
\][/tex]
Combine the [tex]\(x\)[/tex] terms:
[tex]\[
2x^2 - 5x - 12
\][/tex]
Therefore, the simplified expression is:
[tex]\[
2x^2 - 5x - 12
\][/tex]
So, the best answer to the given question is:
C. [tex]\(2x^2 - 5x - 12\)[/tex]
