Which expression is equivalent to (3y - 4)(2y + 7) + 11y - 9? A; 6y^2 + 24y - 37, B; 9y - 37, C; 6y^2 + 11y + 19, D; 16y - 6

To solve this, we need to expand the given expression \((3y - 4)(2y + 7) + 11y - 9\) and simplify it.

### Step 1: Expand the product \((3y - 4)(2y + 7)\)
We apply the distributive property (FOIL method):
\[
(3y)(2y) + (3y)(7) + (-4)(2y) + (-4)(7)
\]
\[
= 6y^2 + 21y - 8y - 28
\]
Now combine like terms:
\[
6y^2 + (21y - 8y) - 28 = 6y^2 + 13y - 28
\]

### Step 2: Add the remaining terms \(+ 11y - 9\) to the expanded result:
\[
6y^2 + 13y - 28 + 11y - 9
\]
Combine the like terms:
\[
6y^2 + (13y + 11y) - (28 + 9) = 6y^2 + 24y - 37
\]

### Conclusion:
The equivalent expression is:
\[
\boxed{6y^2 + 24y - 37}
\]
Thus, the correct answer is **A**.

Do you want more details or have any questions?

Here are 5 related questions to explore:
1. How do you factor quadratic expressions like \(6y^2 + 24y - 37\)?
2. What is the distributive property and how is it used in algebra?
3. How can you simplify complex polynomial expressions?
4. Can you explain the FOIL method in more detail?
5. How do you handle expressions with multiple variables?

**Tip**: Always combine like terms as the final step in simplifying algebraic expressions to avoid missing important simplifications.

Learn how to simplify the expression (3y - 4)(2y + 7) + 11y - 9 with a step-by-step solution using the distributive property and FOIL method. This problem introduces key algebraic concepts such as polynomial expansion and combining like terms. Suitable for Grades 8-10.

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