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Both x and y are integers. Which of the following expression
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30 Jul 2020, 13:37

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

Indicate all such expressions.

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

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

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

Re: Both x and y are integers. Which of the following expression
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31 Jul 2020, 10:00

2

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.

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.

Re: Both x and y are integers. Which of the following expression
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03 Aug 2020, 10:40

Expert Reply

Fixed the typo in the first answer choice.

Thanks for your patient.

Regards

Thanks for your patient.

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Joined: **10 Apr 2015 **

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Re: Both x and y are integers. Which of the following expression
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03 Aug 2020, 15:32

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

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

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Joined: **20 Jun 2019 **

Posts: **181**

Given Kudos: **41 **

Re: Both x and y are integers. Which of the following expression
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05 Aug 2020, 23:34

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.

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!

Re: Both x and y are integers. Which of the following expression
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21 Jan 2024, 13:18

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