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Which expression is equivalent to (5x − 3y)^2?

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Which expression is equivalent to (5x − 3y)^2? [#permalink]

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New post 21 Feb 2017, 23:18
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Which expression is equivalent to (5x − 3y)^2?
A. 10x − 6y
B. 25x − 9y
C. 25x^2 − 9y^2
D. 25x^2 − 15xy + 9y^2
E. 25x^2 − 30xy + 9y^2
[Reveal] Spoiler: OA
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Magoosh GMAT Instructor
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Which expression is equivalent to (5x − 3y)^2? [#permalink]

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New post 22 Feb 2017, 16:37
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vikasp99 wrote:
Which expression is equivalent to (5x − 3y)^2?
A. 10x − 6y
B. 25x − 9y
C. 25x^2 − 9y^2
D. 25x^2 − 15xy + 9y^2
E. 25x^2 − 30xy + 9y^2

Dear vikasp99,

I'm happy to respond. :-) This is a relatively straightforward question testing your basic knowledge of algebra. See this article:
Three Algebra Formulas Essential for the GMAT

The pattern tested here is the Square of a Difference.
\((P - Q)^2 = P^2 - 2PQ + Q^2\)

Here, P = 5x, and Q = 3y, so
\(P^2 = (5x)^2 = 25x^2\)
\(2PQ = 2(5x)(3y) = 30xy\)
\(Q^2 = (3y)^2 = 9y^2\)

Therefore:
\((5x − 3y)^2 = 25x^2 − 30xy + 9y^2\)

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

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Which expression is equivalent to (5x − 3y)^2?   [#permalink] 22 Feb 2017, 16:37
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Which expression is equivalent to (5x − 3y)^2?

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