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If x-2y=4, then x^2-4xy+4y^2-x+2y=?

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If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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New post 21 Jan 2019, 01:22
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[Math Revolution GMAT math practice question]

If \(x-2y=4\), then \(x^2-4xy+4y^2-x+2y=\)?

\(A. 12\)
\(B. 16\)
\(C. 20\)
\(D. 24\)
\(E. 28\)

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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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New post 21 Jan 2019, 01:25
\((x-2y)^2 = x^2-4xy+4y^2\) = 16
\(x^2−4xy+4y^2−x+2y\) = 16-4 = 12

A is the answer.
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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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New post 21 Jan 2019, 04:36
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x-2y=4\), then \(x^2-4xy+4y^2-x+2y=\)?

\(A. 12\)
\(B. 16\)
\(C. 20\)
\(D. 24\)
\(E. 28\)


Let \(x=4\) and \(y=0\), with the result that \(x-2y=4\).
Plugging \(x=4\) and \(y=0\) into \(x^2-4xy+4y^2-x+2y=\), we get:
\(4^2-0+0-4+0=12\)


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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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New post 21 Jan 2019, 05:38
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x-2y=4\), then \(x^2-4xy+4y^2-x+2y=\)?

\(A. 12\)
\(B. 16\)
\(C. 20\)
\(D. 24\)
\(E. 28\)

\(x - 2y = 4\,\,\,\,\,\left( * \right)\)

\(? = \underbrace {{x^2} - 4xy + 4{y^2}}_{{{\left( {x - 2y} \right)}^2}} - x + 2y\)

\(? = {\left( {x - 2y} \right)^2} - \left( {x - 2y} \right)\,\,\,\mathop = \limits_{{\rm{twice}}}^{\left( * \right)} \,\,\,16 - 4 = 12\)


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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New post 21 Jan 2019, 07:56
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x-2y=4\), then \(x^2-4xy+4y^2-x+2y=\)?

\(A. 12\)
\(B. 16\)
\(C. 20\)
\(D. 24\)
\(E. 28\)


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
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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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New post 21 Jan 2019, 08:06
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x-2y=4\), then \(x^2-4xy+4y^2-x+2y=\)?

\(A. 12\)
\(B. 16\)
\(C. 20\)
\(D. 24\)
\(E. 28\)


IMO A

\(x^2-4xy+4y^2-x+2y\)
\(x^2-4xy+4y^2-(x-2y)\) (a)

x-2y = 4
squaring both sides
\(x^2-4xy+4y^2=16\)

substituting above in (a)
16 - 4
12
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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?  [#permalink]

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New post 23 Jan 2019, 01:09
=>

\(x^2-4xy+4y^2-x+2y\)
\(=(x-2y)^2 – (x-2y)\)
\(=4^2 – 4 = 16 – 4 = 12.\)

Therefore, the answer is A.
Answer: A
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Re: If x-2y=4, then x^2-4xy+4y^2-x+2y=?   [#permalink] 23 Jan 2019, 01:09
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