Answer :
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]
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]
