shawnashawn4
Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Select the correct answer.

Which expression is equivalent to the given expression?
[tex]\[ (3y - 4)(2y + 7) + 11y - 9 \][/tex]

A. [tex]\( 6y^2 + 24y - 37 \)[/tex]

B. [tex]\( 9y - 37 \)[/tex]

C. [tex]\( 16y - 6 \)[/tex]

D. [tex]\( 6y^2 + 11y + 19 \)[/tex]

Sagot :

GinnyAnswer
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]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.