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If x is negative and y is positive, what is 4x2−4xy+y2

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If x is negative and y is positive, what is 4x2−4xy+y2  [#permalink]

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New post 28 May 2019, 03:41
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If \(x\) is negative and \(y\) is positive, what is \(\sqrt{4x^2−4xy+y^2}\) ?

A. \(2x−y\)
B. \(2x+y\)
C. \(y−2x\)
D. \(2x+2\)
E. \(2x−2y\)

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Re: If x is negative and y is positive, what is 4x2−4xy+y2  [#permalink]

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New post 28 May 2019, 04:31
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Re: If x is negative and y is positive, what is 4x2−4xy+y2  [#permalink]

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New post 28 May 2019, 04:01
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It is the square of (2x-y) or (y-2x) . Since y is positive and x is negative it should be (y-2x).

Ps You cannot take root of a negative number.

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Re: If x is negative and y is positive, what is 4x2−4xy+y2  [#permalink]

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New post 28 May 2019, 05:37
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PriyankaPalit7 wrote:
If \(x\) is negative and \(y\) is positive, what is \(\sqrt{4x^2−4xy+y^2}\) ?

A. \(2x−y\)
B. \(2x+y\)
C. \(y−2x\)
D. \(2x+2\)
E. \(2x−2y\)


Concept used
(a-b)^2 = a^2 + b^2 -2ab
lxl = \sqrt{x^2}

Given expression can be reduced to l2x-yl;
Now x is -ve and y is +ve= (y-2x) C
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If x is negative and y is positive, what is 4x2−4xy+y2  [#permalink]

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New post 29 May 2019, 17:42
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PriyankaPalit7 wrote:
If \(x\) is negative and \(y\) is positive, what is \(\sqrt{4x^2−4xy+y^2}\) ?

A. \(2x−y\)
B. \(2x+y\)
C. \(y−2x\)
D. \(2x+2\)
E. \(2x−2y\)


Use the answers:

x = -2
y = 1

\(\sqrt{4(-2)^2−4(-2)(1)+1^2}\) = 5

A. \(2x−y\) = \(2(-2)−(1)\) = -5 ... discard
B. \(2x+y\) = \(2(-2)+1\) = -3 ... discard
C. \(y−2x\) = \(1−2(-2)\) = 5 ... hold
D. \(2x+2\) = \(2(-2)+2\) = -2 ... discard
E. \(2x−2y\) = \(2(-2)−2(1)\) = -6 ... discard

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Re: If x is negative and y is positive, what is 4x2−4xy+y2  [#permalink]

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New post 29 May 2019, 22:21
The common mistake being tested here is that we always forget that square root is always positive i.e. \(\sqrt{y^2}\)= |y|
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Re: If x is negative and y is positive, what is 4x2−4xy+y2  [#permalink]

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New post 03 Oct 2019, 15:58
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Test x=-1 and y=1 to find 3
plug-in x=-1 and y=1 into each answer choice to find the correct answer.
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Re: If x is negative and y is positive, what is 4x2−4xy+y2   [#permalink] 03 Oct 2019, 15:58
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