To simplify the given expression [tex]\( (3y - 4)(2y + 7) + 11y - 9 \)[/tex], follow these steps:
1. Expand the product [tex]\( (3y - 4)(2y + 7) \)[/tex]:
[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]
[tex]\[
= 6y^2 + 13y - 28
\][/tex]
2. Add the remaining terms [tex]\( + 11y - 9 \)[/tex] to the expanded expression:
[tex]\[
6y^2 + 13y - 28 + 11y - 9
\][/tex]
3. Combine like terms (terms with [tex]\( y \)[/tex]):
[tex]\[
6y^2 + (13y + 11y) - 28 - 9
\][/tex]
[tex]\[
6y^2 + 24y - 37
\][/tex]
Thus, the simplified expression is:
[tex]\[
6y^2 + 24y - 37
\][/tex]
The correct answer is:
A. [tex]\( 6y^2 + 24y - 37 \)[/tex]
