What is the product of the binomials [tex]\((4a - 1)\)[/tex] and [tex]\((2b + 3)\)[/tex]?

A. [tex]\(18ab - 3\)[/tex]
B. [tex]\(8a^2b^2 + 10ab - 3\)[/tex]
C. [tex]\(6ab + 7a - 2b - 3\)[/tex]
D. [tex]\(8ab + 12a - 2b - 3\)[/tex]



Answer :

To find the product of the binomials [tex]\((4a - 1)\)[/tex] and [tex]\((2b + 3)\)[/tex], proceed with the distributive property, also known as the FOIL method (First, Outer, Inner, Last) for binomials:

1. First terms: Multiply the first terms of each binomial.
[tex]\[ 4a \cdot 2b = 8ab \][/tex]

2. Outer terms: Multiply the outer terms of the binomials.
[tex]\[ 4a \cdot 3 = 12a \][/tex]

3. Inner terms: Multiply the inner terms of the binomials.
[tex]\[ -1 \cdot 2b = -2b \][/tex]

4. Last terms: Multiply the last terms of each binomial.
[tex]\[ -1 \cdot 3 = -3 \][/tex]

Now, add these products together:
[tex]\[ 8ab + 12a - 2b - 3 \][/tex]

So, the fully expanded form of the product [tex]\((4a - 1)(2b + 3)\)[/tex] is:
[tex]\[ 8ab + 12a - 2b - 3 \][/tex]

Hence, the correct answer is:
[tex]\[ \boxed{8ab + 12a - 2b - 3} \][/tex]