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xy > 0
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20 May 2018, 13:57
20 May 2018, 13:57
Expert Reply
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Question Stats:
80% (00:44) correct
19% (00:49) wrong based on 87 sessions
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xy > 0
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\((2x - y)(x + 4y)\) |
\(2x^2 + 8xy - 4y^2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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Re: xy > 0
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03 Nov 2018, 09:20
03 Nov 2018, 09:20
2
sandy wrote:
xy > 0
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\((2x - y)(x + 4y)\) |
\(2x^2 + 8xy - 4y^2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
We can solve this question using matching operations
Given:
Quantity A: (2x - y)(x + 4y)
Quantity B: 2x² + 8xy - 4y²
Use FOIL to expand Quantity A:
Quantity A: 2x² + 8xy - xy - 4y²
Quantity B: 2x² + 8xy - 4y²
Subtract 2x² from both sides to get:
Quantity A: 8xy - xy - 4y²
Quantity B: 8xy - 4y²
Subtract 8xy from both sides to get:
Quantity A: -xy - 4y²
Quantity B: -4y²
Add 4y² to both sides to get:
Quantity A: -xy
Quantity B: 0
IMPORTANT: We're told that xy > 0
In other words, xy = some POSITIVE number, which means -xy = some NEGATIVE number
We get:
Quantity A: some NEGATIVE number
Quantity B: 0
Answer: B
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Re: xy > 0
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03 Nov 2018, 22:24
03 Nov 2018, 22:24
Expert Reply
1
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sandy wrote:
xy > 0
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\((2x - y)(x + 4y)\) |
\(2x^2 + 8xy - 4y^2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
(\(A=(2x - y)(x + 4y)=2x^2=8xy-xy-4y^2=2x^2 + 7xy - 4y^2\)) and (\(B=2x^2 + 8xy - 4y^2\))
now the comparison is between 7xy and 8xy.
since xy > 0, and 8xy-7xy=xy we can write 8xy-7xy instead of xy, so xy>0 becomes 8xy-7xy>0....8xy>7xy OR B>A
B
