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# (x - 2y)(x + 2y) = 4

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(x - 2y)(x + 2y) = 4 [#permalink]  01 Feb 2017, 06:51
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Expert's post
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Question Stats:

94% (00:11) correct 5% (01:37) wrong based on 19 sessions

$$(x - 2y)(x + 2y) = 4$$

 Quantity A Quantity B $$x^2 - 4y^2$$ $$8$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: (x - 2y)(x + 2y) = 4 [#permalink]  06 Feb 2017, 09:28
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Expert's post
Explanation

We know that, $$(x + y)(x - y) = x^2 - y^2$$

So we can rewrite the:

$$(x + 2y)(x - 2y) = x^2 - 4y^2 = 4$$

They can quickly compare 4 to 8 and determine B is greater.

If you forget the classic quadratic form, simply perform (first, outer, inner, last):

(x + 2y)(x - 2y) → $$x^2 - 2xy + 2xy - 4y^2 = 4$$ → $$x^2 - 4y^2 = 4$$

Compare the quantities: Quantity A: 4 Quantity B: 8

Hence option B is correct.
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Re: (x - 2y)(x + 2y) = 4   [#permalink] 06 Feb 2017, 09:28
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