Sure, let's multiply the two binomials step-by-step.
Given:
[tex]\[
(x - 6)(5x - 4)
\][/tex]
We will use the distributive property (also known as the FOIL method for binomials: First, Outer, Inner, Last) to multiply these two binomials.
1. First: Multiply the first terms in each binomial:
[tex]\[
x \cdot 5x = 5x^2
\][/tex]
2. Outer: Multiply the outer terms in the binomials:
[tex]\[
x \cdot (-4) = -4x
\][/tex]
3. Inner: Multiply the inner terms in the binomials:
[tex]\[
-6 \cdot 5x = -30x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
-6 \cdot (-4) = 24
\][/tex]
Next, we add all these results together:
[tex]\[
5x^2 + (-4x) + (-30x) + 24
\][/tex]
Combine the like terms [tex]\((-4x\)[/tex] and [tex]\(-30x\)[/tex]):
[tex]\[
5x^2 - 34x + 24
\][/tex]
So, the product of [tex]\((x - 6)(5x - 4)\)[/tex] is:
[tex]\[
5x^2 - 34x + 24
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{B. \; 5x^2 - 34x + 24}
\][/tex]
