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

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Senior Manager
Joined: 02 Jan 2017
Posts: 312
Which expression is equivalent to (5x − 3y)^2?  [#permalink]

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21 Feb 2017, 23:18
00:00

Difficulty:

5% (low)

Question Stats:

89% (00:41) correct 11% (00:59) wrong based on 56 sessions

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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
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4488
Which expression is equivalent to (5x − 3y)^2?  [#permalink]

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22 Feb 2017, 16:37
1
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

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

CEO
Joined: 11 Sep 2015
Posts: 3113
Re: Which expression is equivalent to (5x − 3y)^2?  [#permalink]

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07 Apr 2018, 05:05
Top Contributor
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

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

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com

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