Sure! Let's simplify the given expression step by step to determine which of the provided options is equivalent to it.
Given:
[tex]\[
(3y - 4)(2y + 7) + 11y - 9
\][/tex]
Step 1: Expand the product [tex]\((3y - 4)(2y + 7)\)[/tex].
Using the distributive property (also known as the FOIL method for binomials):
[tex]\[
(3y - 4)(2y + 7) = 3y \cdot 2y + 3y \cdot 7 - 4 \cdot 2y - 4 \cdot 7
\][/tex]
[tex]\[
= 6y^2 + 21y - 8y - 28
\][/tex]
Combine like terms:
[tex]\[
= 6y^2 + (21y - 8y) - 28
\][/tex]
[tex]\[
= 6y^2 + 13y - 28
\][/tex]
Step 2: Add the remaining terms in the original expression:
[tex]\[
6y^2 + 13y - 28 + 11y - 9
\][/tex]
Combine like terms again:
[tex]\[
6y^2 + (13y + 11y) - 28 - 9
\][/tex]
[tex]\[
= 6y^2 + 24y - 37
\][/tex]
So, the expression simplifies to:
[tex]\[
6y^2 + 24y - 37
\][/tex]
Conclusion: The expression equivalent to [tex]\((3y-4)(2y+7) + 11y - 9\)[/tex] is:
[tex]\[
6y^2 + 24y - 37
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{A. \; 6y^2 + 24y - 37}
\][/tex]
