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Difference of two squares
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Updated on: 31 Aug 2017, 02:23
Updated on: 31 Aug 2017, 02:23
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Question Stats:
72% (00:56) correct
27% (00:56) wrong based on 85 sessions
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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.
Re: Difference of two squares
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29 Aug 2017, 04:16
29 Aug 2017, 04:16
1
Expert Reply
jcudjo1 wrote:
Quantity A
(x^2+y^2)(x^2-y^2)
Quantity B
(x^3+y^3)(x-y)
(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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Difference of two squares
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01 Sep 2017, 13:29
01 Sep 2017, 13:29
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
Answer: D
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