To multiply the binomials [tex]\((3x + 4)(5x - 2)\)[/tex], we use the distributive property (also known as the FOIL method for binomials):
1. First: Multiply the first terms in each binomial:
[tex]\[
3x \cdot 5x = 15x^2
\][/tex]
2. Outer: Multiply the outer terms in each binomial:
[tex]\[
3x \cdot (-2) = -6x
\][/tex]
3. Inner: Multiply the inner terms in each binomial:
[tex]\[
4 \cdot 5x = 20x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
4 \cdot (-2) = -8
\][/tex]
Next, we combine all these results:
[tex]\[
15x^2 - 6x + 20x - 8
\][/tex]
Combine the middle terms [tex]\(-6x\)[/tex] and [tex]\(20x\)[/tex]:
[tex]\[
-6x + 20x = 14x
\][/tex]
Thus, the expanded form of the binomials is:
[tex]\[
15x^2 + 14x - 8
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{15x^2 + 14x - 8}
\][/tex]
So, the correct option is D.
