The area of a rectangle is calculated as 4x2 - 16y2 square units. Which of the choices below could be the dimensions of the rectangle? O (2x+4y) and (2x - 4y) O (x+y) and (2x-2y) O (2x-4y) and (2x-2y) O (x+y) and (2x - 4y)
The area of a rectangle is calculated as 4x2 - 16y2 square units. Which of the choices below could be the dimensions of the rectangle? O (2x+4y) and (2x - 4y) O (x+y) and (2x-2y) O (2x-4y) and (2x-2y) O (x+y) and (2x - 4y)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![The problem states:
"The area of a rectangle is calculated as \(4x^2 - 16y^2\) square units. Which of the choices below could be the dimensions of the rectangle?"
Options:
A) \((2x + 4y)\) and \((2x - 4y)\)
B) \((x + y)\) and \((2x - 2y)\)
C) \((2x - 4y)\) and \((2x - 2y)\)
D) \((x + y)\) and \((2x - 4y)\)
### Explanation:
The expression for the area of the rectangle, \(4x^2 - 16y^2\), resembles a difference of squares. This can be factored as follows:
\[4x^2 - 16y^2 = (2x)^2 - (4y)^2 = (2x + 4y)(2x - 4y)\]
Thus, the dimensions that could correspond to the rectangle are \((2x + 4y)\) and \((2x - 4y)\), which matches option A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5feef8a3-4722-4969-8d03-b0e4b16fec00%2F360cc309-9dfd-4616-b229-e5b52bfcba17%2Fgq0nd4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The problem states:
"The area of a rectangle is calculated as \(4x^2 - 16y^2\) square units. Which of the choices below could be the dimensions of the rectangle?"
Options:
A) \((2x + 4y)\) and \((2x - 4y)\)
B) \((x + y)\) and \((2x - 2y)\)
C) \((2x - 4y)\) and \((2x - 2y)\)
D) \((x + y)\) and \((2x - 4y)\)
### Explanation:
The expression for the area of the rectangle, \(4x^2 - 16y^2\), resembles a difference of squares. This can be factored as follows:
\[4x^2 - 16y^2 = (2x)^2 - (4y)^2 = (2x + 4y)(2x - 4y)\]
Thus, the dimensions that could correspond to the rectangle are \((2x + 4y)\) and \((2x - 4y)\), which matches option A.
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