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Choose the correct answer.

Which expression is equivalent to the given expression?

[tex]\[
(3y - 4)(2y + 7) + 11y - 9
\][/tex]

A. [tex]\[16y - 6\][/tex]

B. [tex]\[6y^2 + 24y - 37\][/tex]

C. [tex]\[6y^2 + 11y + 18\][/tex]

D. [tex]\[9y - 37\][/tex]

Sagot :

GinnyAnsweridn
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]
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