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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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28 May 2019, 03:41
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Difficulty:

55% (hard)

Question Stats:

55% (01:31) correct 45% (01:26) wrong based on 164 sessions

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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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28 May 2019, 04:31
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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. $$2x−2y$$

$$\sqrt{4x^2−4xy+y^2}=\sqrt{(2x-y)^2}=|2x - y|$$

Since x is negative and y is positive, then 2x - y = negative - positive = negative. Thus, |2x - y| = -(2x - y) = y - 2x.

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

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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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28 May 2019, 05:37
1
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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29 May 2019, 17:42
1
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. $$2x−2y$$

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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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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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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