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If x-2y=4, then x^2-4xy+4y^2-x+2y=?
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19 Feb 2021, 09:29
19 Feb 2021, 09:29
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Question Stats:
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If \(x-2y=4\), then \(x^2-4xy+4y^2-x+2y=\)?
\(A. 12\)
\(B. 16\)
\(C. 20\)
\(D. 24\)
\(E. 28\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
\(A. 12\)
\(B. 16\)
\(C. 20\)
\(D. 24\)
\(E. 28\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
If x-2y=4, then x^2-4xy+4y^2-x+2y=?
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19 Feb 2021, 10:08
19 Feb 2021, 10:08
1
Hi,
The first part of the equation i.e \(x^2−4xy+4y^2\) is nothing but the square of x-2y
Thus squaring x-2y=4 gives us\( x^2−4xy+4y^2\)=16
Now to get the other half we can multiply x-2y=4 by -1 to get -x+2y=-4
Using the two values we get 16-4=12
IMO A
Hope this helps!
The first part of the equation i.e \(x^2−4xy+4y^2\) is nothing but the square of x-2y
Thus squaring x-2y=4 gives us\( x^2−4xy+4y^2\)=16
Now to get the other half we can multiply x-2y=4 by -1 to get -x+2y=-4
Using the two values we get 16-4=12
IMO A
Hope this helps!
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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?
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19 Feb 2021, 10:13
19 Feb 2021, 10:13
1
Carcass wrote:
If \(x-2y=4\), then \(x^2-4xy+4y^2-x+2y=\)?
\(A. 12\)
\(B. 16\)
\(C. 20\)
\(D. 24\)
\(E. 28\)
\(A. 12\)
\(B. 16\)
\(C. 20\)
\(D. 24\)
\(E. 28\)
GIVEN: x - 2y = 4
We want to find the value of x² - 4xy + 4y² - x + 2y
We should notice that x² - 4xy + 4y² is equal to (x - 2y)²
We should notice that - x + 2y is equal to -(x - 2y)
We get: x² - 4xy + 4y² - x + 2y = (x - 2y)² - (x - 2y)
Now replace x - 2y with 4 to get: = (x - 2y)² - (x - 2y) = = (4)² - (4)
= 16 - 4
= 12
Answer: A
Cheers,
Brent
