Answer :
To determine which expression is equivalent to the given expression [tex]\((3y - 4)(2y + 7) + 11y - 9\)[/tex], let's go through the process of expanding and simplifying it step-by-step:
1. Distribute [tex]\((3y - 4)\)[/tex] across [tex]\((2y + 7)\)[/tex]:
[tex]\[ (3y - 4)(2y + 7) = (3y \cdot 2y) + (3y \cdot 7) + (-4 \cdot 2y) + (-4 \cdot 7) \][/tex]
This simplifies to:
[tex]\[ (3y \cdot 2y) + (3y \cdot 7) + (-4 \cdot 2y) + (-4 \cdot 7) = 6y^2 + 21y - 8y - 28 \][/tex]
2. Combine like terms within the result:
[tex]\[ 6y^2 + 21y - 8y - 28 = 6y^2 + 13y - 28 \][/tex]
3. Add the remaining terms [tex]\(11y - 9\)[/tex] to the simplified expression:
[tex]\[ 6y^2 + 13y - 28 + 11y - 9 \][/tex]
4. Combine like terms again:
[tex]\[ 6y^2 + (13y + 11y) - 28 - 9 = 6y^2 + 24y - 37 \][/tex]
Therefore, the expression equivalent to [tex]\((3y - 4)(2y + 7) + 11y - 9\)[/tex] is:
[tex]\[ 6y^2 + 24y - 37 \][/tex]
The correct answer is:
[tex]\[ \boxed{D. \ 6y^2 + 24y - 37} \][/tex]
1. Distribute [tex]\((3y - 4)\)[/tex] across [tex]\((2y + 7)\)[/tex]:
[tex]\[ (3y - 4)(2y + 7) = (3y \cdot 2y) + (3y \cdot 7) + (-4 \cdot 2y) + (-4 \cdot 7) \][/tex]
This simplifies to:
[tex]\[ (3y \cdot 2y) + (3y \cdot 7) + (-4 \cdot 2y) + (-4 \cdot 7) = 6y^2 + 21y - 8y - 28 \][/tex]
2. Combine like terms within the result:
[tex]\[ 6y^2 + 21y - 8y - 28 = 6y^2 + 13y - 28 \][/tex]
3. Add the remaining terms [tex]\(11y - 9\)[/tex] to the simplified expression:
[tex]\[ 6y^2 + 13y - 28 + 11y - 9 \][/tex]
4. Combine like terms again:
[tex]\[ 6y^2 + (13y + 11y) - 28 - 9 = 6y^2 + 24y - 37 \][/tex]
Therefore, the expression equivalent to [tex]\((3y - 4)(2y + 7) + 11y - 9\)[/tex] is:
[tex]\[ 6y^2 + 24y - 37 \][/tex]
The correct answer is:
[tex]\[ \boxed{D. \ 6y^2 + 24y - 37} \][/tex]
