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

[VJesus12]

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

The OA is E .

Seems like I make the calculations wrong. I got D. Can anyone help me? Thanks.

[Sionainn@PrincetonReview]

Yes it looks like you may have not multiplied one of the set of terms.

$$^{(5x-3y)^2}$$
= (5x - 3y)(5x - 3y)

We need to make sure we multiply all of the terms in the first set of parentheses by all of the terms in the second set. A common mnemonic folks use to make sure they multiply all the terms once is FOIL (first, outer, inner and last).

Multiply the FIRST term in each binomial: (5x)(5x) = $$^{25x^2}$$
Multiply the OUTER term (be careful with signs): (5x)(-3y) = -15xy
Multiply the INNER term (be careful with signs): (-3y)(5x) = -15xy
Then, multiply the LAST term in each binomial: (-3y)(-3y) = $$^{9y^2}$$

Finally combine the terms: $$^{25x^2}$$ + (-15xy) + (-15xy) + $$^{9y^2}$$ = $$^{25x^2}$$ - 30xy + $$^{9y^2}$$

Make sense?

Take care,

Sionainn Marcoux,
BA - Stanford University, MPP - Harvard University
Instructor, tutor for Princeton Review and Airbnb host
In other words a blend of Jamie Escalante from Stand and Deliver, Julie from The Love Boat, and Schneider the Super from One Day at a Time.

[Brent@GMATPrepNow]

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

[Scott@TargetTestPrep]

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

Let's expand the given expression:

(5x - 3y)^2 = (5x - 3y)(5x - 3y) = 25x^2 - 30xy + 9y^2

Answer: E