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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]
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