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]
