Last visit was: 20 Nov 2024, 09:37 It is currently 20 Nov 2024, 09:37

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 29991
Own Kudos [?]: 36307 [2]
Given Kudos: 25921
Send PM
User avatar
Manager
Manager
Joined: 02 May 2020
Posts: 91
Own Kudos [?]: 140 [0]
Given Kudos: 0
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 29991
Own Kudos [?]: 36307 [0]
Given Kudos: 25921
Send PM
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12193 [2]
Given Kudos: 136
Send PM
Re: Both x and y are integers. Which of the following expression [#permalink]
2
Carcass wrote:
Both x and y are integers. Which of the following expressions must be the square of an integer?

Indicate all such expressions.


A. \((x+y)(x-y)+8xy+17y^2\)

B. \(9x^4-12x^2y^2+4y^4\)

C. \(x^6+2x^3y^3+y^6\)


A. Given: \((x+y)(x-y)+8xy+17y^2\)
Expand and simplify the first product: \(x^2-y^2+8xy+17y^2\)
Simplify: \(x^2+8xy+16y^2\)
Factor: \((x + 4y)(x + 4y) = (x + 4y)^2\)
WORKS!


B. Given: \(9x^4-12x^2y^2+4y^4\)
Factor to get: \((3x^2-2y^2)(3x^2-2y^2) = (3x^2-2y^2)^2\)
WORKS!


C. Given: \(x^6+2x^3y^3+y^6\)
Factor to get: \((x^3+y^3)(x^3+y^3) = (x^3+y^3)^2\)[/quote]
WORKS!

Answer: A, B, C

Cheers,
Brent
Manager
Manager
Joined: 20 Jun 2019
Posts: 181
Own Kudos [?]: 221 [0]
Given Kudos: 41
GRE 1: Q160 V161

GRE 2: Q165 V159
Send PM
Re: Both x and y are integers. Which of the following expression [#permalink]
rishabhrbs96 wrote:
How come A is correct. If we take x=1 and y=1, expression A will be 8 which is not square of any integer.

B is correct because we can factorize it as (3x^2 - 2y^2)^2

C is correct because we can factorize it as (x^3 + y^3)^2

So, the answers should be B and C.


By your own analogy for A ((x+y)(x−y)+8xy+17y^2) becomes 2*0=0+8*1*1=8+17=25, which is 5^2.

Thanks!
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5022
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: Both x and y are integers. Which of the following expression [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
Re: Both x and y are integers. Which of the following expression [#permalink]
Moderators:
GRE Instructor
83 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne