To solve this problem, we need to simplify and combine the given algebraic expression [tex]\((3y - 4)(2y + 7) + 11y - 9\)[/tex]. We will follow these steps carefully:
1. Expand the product [tex]\((3y - 4)(2y + 7)\)[/tex].
- We use the distributive property (also known as FOIL for binomials) to expand:
[tex]\[
(3y - 4)(2y + 7)
\][/tex]
- Multiply each term in the first binomial by each term in the second binomial:
[tex]\[
3y \cdot 2y + 3y \cdot 7 + (-4) \cdot 2y + (-4) \cdot 7
\][/tex]
- Simplify the products:
[tex]\[
6y^2 + 21y - 8y - 28
\][/tex]
- Combine like terms:
[tex]\[
6y^2 + 13y - 28
\][/tex]
2. Add the remaining terms [tex]\(11y - 9\)[/tex] to the expanded expression:
- Combine the constants and the like terms involving [tex]\(y\)[/tex]:
[tex]\[
(6y^2 + 13y - 28) + 11y - 9
\][/tex]
- Group the like terms:
[tex]\[
6y^2 + (13y + 11y) - 28 - 9
\][/tex]
- Combine the like terms:
[tex]\[
6y^2 + 24y - 37
\][/tex]
Thus, the simplified expression is:
[tex]\[
6y^2 + 24y - 37
\][/tex]
So, the correct option is:
[tex]\[
\text{A. } 6y^2 + 24y - 37
\][/tex]
