Let's multiply the binomials [tex]\((x - 4)(2x + 3)\)[/tex] using the FOIL method, which stands for First, Outer, Inner, Last. This method helps us remember how to multiply each term in the binomials.
1. First: Multiply the first terms in each binomial:
[tex]\[
x \cdot 2x = x(2x)
\][/tex]
2. Outer: Multiply the outer terms in the product:
[tex]\[
x \cdot 3 = x(3)
\][/tex]
3. Inner: Multiply the inner terms in the product:
[tex]\[
-4 \cdot 2x = (-4)(2x)
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
-4 \cdot 3 = (-4)(3)
\][/tex]
Combining all the products together, we get:
[tex]\[
x(2x) + x(3) + (-4)(2x) + (-4)(3)
\][/tex]
Thus, the correct answer choice that shows the FOIL method products is:
B. [tex]\((x)(2 x)+3(x)+(-4)(2 x)+(-4)(3)\)[/tex]
