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# Difference of two squares

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Difference of two squares [#permalink]  28 Aug 2017, 09:17
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Question Stats:

76% (00:38) correct 23% (00:19) wrong based on 21 sessions
 Quantity A Quantity B $$(x^2+y^2)(x^2-y^2)$$ $$(x^3+y^3)(x-y)$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

Last edited by Carcass on 31 Aug 2017, 02:23, edited 1 time in total.
Edited by Carcass
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Re: Difference of two squares [#permalink]  29 Aug 2017, 04:16
1
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Expert's post
jcudjo1 wrote:
Quantity A
(x^2+y^2)(x^2-y^2)

Quantity B
(x^3+y^3)(x-y)

This question is ideal for substitution.
Put x=1 and y=1

Quanity A is 0

Quanity B is 0

Both quantities are equal

Now put Put x=2 and y=1 and evaluate!

Quanity A is 15

Quanity B is 9

Now Quantity A is greater.

Hence D is correct option
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Re: Difference of two squares [#permalink]  01 Sep 2017, 13:29
Expert's post
jcudjo1 wrote:
 Quantity A Quantity B $$(x^2+y^2)(x^2-y^2)$$ $$(x^3+y^3)(x-y)$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Sandy's approach is DEFINITELY the best/fastest approach.
However, if you didn't think of that approach, we can also expand each quantity using the F.O.I.L. method (although it takes a while!).

Given:
Quantity A: (x² + y²)(x² - y²)
Quantity B: (x³ + y³)(x - y)

Expand using FOIL:
Quantity A: x⁴ - x²y² + x²y² - y⁴
Quantity B: x⁴ - x³y + xy³ - y⁴

Simplify:
Quantity A: x⁴ - y⁴
Quantity B: x⁴ - x³y + xy³ - y⁴

Subtract x⁴ from both sides to get:
Quantity A: -y⁴
Quantity B: -x³y + xy³ - y⁴

Add y⁴ to both sides to get:
Quantity A: 0
Quantity B: -x³y + xy³

At this point, we plug in values for x and y

If x = 0 and y = 0, we get:
Quantity A: 0
Quantity B: 0
The quantities are EQUAL

If x = 1 and y = 2, we get:
Quantity A: 0
Quantity B: 6
Quantity B is greater

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Re: Difference of two squares   [#permalink] 01 Sep 2017, 13:29
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