To find the product of the binomials [tex]\((5r + 2)(3r - 4)\)[/tex], we need to use the distributive property, often called the FOIL (First, Outer, Inner, Last) method for binomials. Let's break it down step-by-step:
1. First terms:
Multiply the first terms in each binomial:
[tex]\[
5r \cdot 3r = 15r^2
\][/tex]
2. Outer terms:
Multiply the outer terms in the binomial product:
[tex]\[
5r \cdot (-4) = -20r
\][/tex]
3. Inner terms:
Multiply the inner terms in the binomial product:
[tex]\[
2 \cdot 3r = 6r
\][/tex]
4. Last terms:
Multiply the last terms in each binomial:
[tex]\[
2 \cdot (-4) = -8
\][/tex]
5. Combine all these results:
Add up all the products from steps 1 through 4:
[tex]\[
15r^2 - 20r + 6r - 8
\][/tex]
6. Simplify the expression:
Combine like terms:
[tex]\[
15r^2 - 20r + 6r = 15r^2 - 14r
\][/tex]
Therefore, placing it all together:
[tex]\[
15r^2 - 14r - 8
\][/tex]
Thus, the product of [tex]\((5r + 2)(3r - 4)\)[/tex] is [tex]\(\boxed{15r^2 - 14r - 8}\)[/tex].
