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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: 53020
If x – y = p, then 2x^2 − 4xy + 2y^2 =  [#permalink]

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20 May 2017, 05:54
00:00

Difficulty:

25% (medium)

Question Stats:

74% (00:59) correct 26% (01:06) wrong based on 112 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: 11 Sep 2015
Posts: 3438
Re: If x – y = p, then 2x^2 − 4xy + 2y^2 =  [#permalink]

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20 May 2017, 06:21
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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Manager
Joined: 12 Jun 2016
Posts: 215
Location: India
WE: Sales (Telecommunications)
If x – y = p, then 2x^2 − 4xy + 2y^2 =  [#permalink]

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20 May 2017, 06:23
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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Manager
Joined: 30 Apr 2013
Posts: 78
Re: If x – y = p, then 2x^2 − 4xy + 2y^2 =  [#permalink]

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27 Aug 2017, 00:15
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: 53020
Re: If x – y = p, then 2x^2 − 4xy + 2y^2 =  [#permalink]

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27 Aug 2017, 02:01
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 =  [#permalink]

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08 Feb 2019, 20:18
Bunuel wrote:
If $$x – y = p$$, then $$2x^2 − 4xy + 2y^2 =$$

(A) p

(B) 2p

(C) 4p

(D) p^2

(E) 2p^2

Take 2 common $$2x^2 − 4xy + 2y^2 =$$

2 * (x-y)^2

2 * p^2

E
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Re: If x – y = p, then 2x^2 − 4xy + 2y^2 =   [#permalink] 08 Feb 2019, 20:18
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