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For real numbers a and b, define a?b = (a - b)^2. What is (x - y)^2 ?

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Bunuel
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For real numbers a and b, define a?b = (a - b)^2. What is (x - y)^2 ? [#permalink] New post   27 Mar 2019, 20:57
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A
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Question Stats:

86% (01:44) correct 14% (02:22) wrong based on 84 sessions
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For all numbers a and b, define a?b = (a - b)^2. What is (x - y)^2 ? (y - x)^2 ?

(A) 0
(B) x^2 + y^2
(C) 2x^2
(D) 2y^2
(E) 4xy
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A
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Re: For real numbers a and b, define a?b = (a - b)^2. What is (x - y)^2 ? [#permalink] New post   27 Mar 2019, 23:27
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raypohan wrote:
a?b = (a - b)^2

(x - y)^2 ? (y - x)^2

Algebra method

= (x - y)^2 ? (y - x)^2
= ((x - y)^2 - (y - x)^2)^2
= (( x^2 -2xy + y^2 ) - ( x^2 -2xy + y^2))^2
= open brackets
= (( x^2 -2xy + y^2 - x^2 + 2xy - y^2))^2
= (0)^2
= 0

Numerical Method
let x & y be an easy number
x = 5
y = 2
= (x - y)^2 ? (y - x)^2
= ((5 - 2)^2 - (2 - 5)^2)^2
= ((3)^2 - (-3)^2)^2
= (9 - 9)^2

Correct me if I'm wrong
Thanks



There's nothing wrong with the solution, but this can be done within seconds when you realise that (x-y)^2 is same as (y-x)^2....

(2-4)^2 is same as (4-2)^2

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Re: For real numbers a and b, define a?b = (a - b)^2. What is (x - y)^2 ? [#permalink] New post   27 Mar 2019, 23:23
a?b = (a - b)^2

(x - y)^2 ? (y - x)^2

Algebra method

= (x - y)^2 ? (y - x)^2
= ((x - y)^2 - (y - x)^2)^2
= (( x^2 -2xy + y^2 ) - ( x^2 -2xy + y^2))^2
= open brackets
= (( x^2 -2xy + y^2 - x^2 + 2xy - y^2))^2
= (0)^2
= 0

Numerical Method
let x & y be an easy number
x = 5
y = 2
= (x - y)^2 ? (y - x)^2
= ((5 - 2)^2 - (2 - 5)^2)^2
= ((3)^2 - (-3)^2)^2
= (9 - 9)^2

Correct me if I'm wrong
Thanks
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Re: For real numbers a and b, define a?b = (a - b)^2. What is (x - y)^2 ? [#permalink] New post   28 Sep 2022, 12:01
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Given that a?b = \((a - b)^2\) and we need to find the value of \((x - y)^2 ? (y - x)^2\)

To find \((x - y)^2 ? (y - x)^2\) we need to compare what is before and after ? in \((x - y)^2 ? (y - x)^2\) and a?b

=> We need to substitute a with \((x - y)^2\) and b with \((y - x)^2\) in a?b = \((a - b)^2\) to get the value of \((x - y)^2 ? (y - x)^2\)

=> \((x - y)^2 ? (y - x)^2\) = \(((x - y)^2 - (y - x)^2)^2\) = \(((x^2 -2xy +y^2) - (x^2 -2xy +y^2))^2\) = 0

So, Answer will be A
Hope it helps!

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Re: For real numbers a and b, define a?b = (a - b)^2. What is (x - y)^2 ? [#permalink]
28 Sep 2022, 12:01
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