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 ySo, 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 =

9So, 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 =

4Let'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