Certainly! Let's go through a detailed, step-by-step solution to find the expression equivalent to:
[tex]\[
(3y - 4)(2y + 7) + 11y - 9
\][/tex]
### Step 1: Expand the First Term
First, we need to 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]
Calculating each term:
[tex]\[
(3y \cdot 2y) = 6y^2
\][/tex]
[tex]\[
(3y \cdot 7) = 21y
\][/tex]
[tex]\[
(-4 \cdot 2y) = -8y
\][/tex]
[tex]\[
(-4 \cdot 7) = -28
\][/tex]
Combining these, we get:
[tex]\[
6y^2 + 21y - 8y - 28 = 6y^2 + 13y - 28
\][/tex]
### Step 2: Add the Remaining Terms
Now, add [tex]\(11y - 9\)[/tex] to the expanded expression:
[tex]\[
6y^2 + 13y - 28 + 11y - 9
\][/tex]
Combine like terms:
[tex]\[
6y^2 + (13y + 11y) - 28 - 9 = 6y^2 + 24y - 37
\][/tex]
### Step 3: Compare to Given Options
We have simplified the given expression to:
[tex]\[
6y^2 + 24y - 37
\][/tex]
Now we compare this with the given options:
- A. [tex]\(16y - 6\)[/tex]
- B. [tex]\(6y^2 + 24y - 37\)[/tex]
- C. [tex]\(6y^2 + 11y + 18\)[/tex]
- D. [tex]\(9y - 37\)[/tex]
The simplified expression [tex]\(6y^2 + 24y - 37\)[/tex] matches option B.
### Conclusion
The expression equivalent to [tex]\((3y - 4)(2y + 7) + 11y - 9\)[/tex] is:
[tex]\[
\boxed{6y^2 + 24y - 37}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{B}
\][/tex]
