Which expression is equivalent to the given expression ? (3y-4) (2y+7) +11y-9
A. 16y-6
B. 6y+11y +19
C. 6y +24y-37
D. 9y-37
The Correct Answer and Explanation is:
To find which expression is equivalent to ((3y – 4)(2y + 7) + 11y – 9), we need to first expand the expression ((3y – 4)(2y + 7)) and then combine like terms with the additional terms (11y) and (-9).
Step 1: Expand ((3y – 4)(2y + 7))
Using the distributive property (also known as the FOIL method for binomials), we can expand:
[
(3y – 4)(2y + 7) = 3y \cdot 2y + 3y \cdot 7 – 4 \cdot 2y – 4 \cdot 7
]
Calculating each term:
- (3y \cdot 2y = 6y^2)
- (3y \cdot 7 = 21y)
- (-4 \cdot 2y = -8y)
- (-4 \cdot 7 = -28)
Combining these results gives:
[
6y^2 + 21y – 8y – 28 = 6y^2 + (21y – 8y) – 28 = 6y^2 + 13y – 28
]
Step 2: Combine with the remaining terms (11y – 9)
Now, add the (11y) and (-9) to the expanded expression:
[
6y^2 + 13y – 28 + 11y – 9
]
Combining like terms gives:
- The (y^2) term: (6y^2)
- The (y) terms: (13y + 11y = 24y)
- The constant terms: (-28 – 9 = -37)
So, the entire expression simplifies to:
[
6y^2 + 24y – 37
]
Step 3: Compare with the given options
Now let’s examine the options provided:
A. (16y – 6)
B. (6y + 11y + 19)
C. (6y + 24y – 37)
D. (9y – 37)
Checking each option:
- Option A is not equivalent as it lacks a (y^2) term.
- Option B simplifies to (17y + 19), which does not match.
- Option C simplifies to (30y – 37) which is also not a match.
- Option D simplifies to (9y – 37), again not equivalent.
The correct equivalent expression is C, when interpreted as (6y^2 + 24y – 37), aligning with the expanded expression. The answer can be clarified if we rephrase or consider the polynomial terms.
Thus, the correct answer is:
C. (6y + 24y – 37) (interpreted in context, matching the (6y^2 + 24y – 37) upon correction).