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# If x – y = p, then 2x^2 − 4xy + 2y^2 =

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Math Expert
Joined: 02 Sep 2009
Posts: 47898
If x – y = p, then 2x^2 − 4xy + 2y^2 =  [#permalink]

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20 May 2017, 06:54
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Difficulty:

25% (medium)

Question Stats:

68% (00:53) correct 32% (00:45) wrong based on 139 sessions

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If $$x – y = p$$, then $$2x^2 − 4xy + 2y^2 =$$

(A) p

(B) 2p

(C) 4p

(D) p^2

(E) 2p^2

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Joined: 12 Sep 2015
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Re: If x – y = p, then 2x^2 − 4xy + 2y^2 =  [#permalink]

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20 May 2017, 07:21
Top Contributor
Bunuel wrote:
If $$x – y = p$$, then $$2x^2 − 4xy + 2y^2 =$$

(A) p

(B) 2p

(C) 4p

(D) p^2

(E) 2p^2

Given: x – y = p

2x² − 4xy + 2y² = 2(x² − 2xy + y²)
= 2(x - y
= 2(p

Cheers,
Brent
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If x – y = p, then 2x^2 − 4xy + 2y^2 =  [#permalink]

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20 May 2017, 07:23
Given : $$(X-Y) = p$$

Squaring both sides we have -
$$X^2+Y^2-2XY = P^2$$

Needed: $$2X^2+2Y^2-4XY = ?$$

$$2X^2+2Y^2-4XY = (X^2+Y^2-2XY )+ (X^2+Y^2-2XY)$$, Substituting we get
$$P^2+P^2 = 2P^2$$

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Re: If x – y = p, then 2x^2 − 4xy + 2y^2 =  [#permalink]

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27 Aug 2017, 01:15
Is it possible to divide the equation by 2 first and then applying (a+b)(a-b) formula
Math Expert
Joined: 02 Sep 2009
Posts: 47898
Re: If x – y = p, then 2x^2 − 4xy + 2y^2 =  [#permalink]

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27 Aug 2017, 03:01
santro789 wrote:
Is it possible to divide the equation by 2 first and then applying (a+b)(a-b) formula

You can factor out 2 first: $$2x^2 − 4xy + 2y^2 =2(x^2-2xy+y^2)=2(x-y)^2=2p^2$$.

You cannot divide by 2 (so you cannot get rid of the 2 altogether) because we need the value of $$2x^2 − 4xy + 2y^2$$ not the value of $$x^2 − 2xy + y^2$$.

Hope it helps.
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Re: If x – y = p, then 2x^2 − 4xy + 2y^2 = &nbs [#permalink] 27 Aug 2017, 03:01
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