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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 22 Feb 2017, 00:18
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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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Which expression is equivalent to (5x − 3y)^2? [#permalink]

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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 :-)
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Mike McGarry
Magoosh Test Prep

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

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New post 07 Apr 2018, 06:05
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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


One option is to use the FOIL method to expand the product (that's the solution I'd typically use)
However, we can also use this approach:

First recognize that we're looking for an expression that's EQUIVALENT to (5x − 3y)^2 for all values of x and y
So, for example, let's determine the value of (5x − 3y)^2 when x = 0 and y = 1
Take (5x − 3y)^2 and replace x with 0 and y with 1 to get: [5(0) − 3(1)]^2 = [−3]^2 = 9

So, the answer choice that's EQUIVALENT to (5x − 3y)^2 must also evaluate to be 9 when x = 0 and y = 1
Let's check each answer choice...

A. 10(0) − 6(1) = -6. ELIMINATE
B. 25(0) − 9(1) = -9. ELIMINATE
C. 25(0^2) − 9(1^2) = -9. ELIMINATE
D. 25(0^2) − 15(0)(1) + 9(1^2) = 9. KEEP
E. 25(0^2) − 30(0)(1) + 9(1^2) = 9. KEEP

Okay, we have two possible answer choices remaining.
We need to plug in ANOTHER set of values.
How about x = 1 and y = 1
Take (5x − 3y)^2 and replace x with 1 and y with 1 to get: [5(1) − 3(1)]^2 = [2]^2 = 4
Let's check the two remaining answer choices...
D. 25(1^2) − 15(1)(1) + 9(1^2) = 19. ELIMINATE
E. 25(1^2) − 30(1)(1) + 9(1^2) = 4. KEEP

Answer: E

Cheers,
Brent
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Brent Hanneson – Founder of gmatprepnow.com

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Re: Which expression is equivalent to (5x − 3y)^2?   [#permalink] 07 Apr 2018, 06:05
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