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a ≠ –b
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15 Apr 2018, 04:34
15 Apr 2018, 04:34
Expert Reply
00:00
Question Stats:
81% (00:46) correct
18% (01:16) wrong based on 43 sessions
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a ≠ –b
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.
Quantity A |
Quantity B |
\(\frac{6a^2+12ab+6b^2}{(a+b)}\) |
\(6(a+b)\) |
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.
Drill 1
Question: 5
Page: 511
Question: 5
Page: 511
Re: a ≠ –b
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18 Apr 2018, 15:44
18 Apr 2018, 15:44
Expert Reply
Explanation
Whenever you see exponents, think common quadratics.
If you factor the 6 out of the numerator in Quantity A, you get \(6(a^2 + 2ab + b^2)\), which includes a common quadratic \((a +b)^2\).
Then you can cancel (a + b) from both the numerator and the denominator; Quantity A is really just 6(a + b). The quantities are equal.
Whenever you see exponents, think common quadratics.
If you factor the 6 out of the numerator in Quantity A, you get \(6(a^2 + 2ab + b^2)\), which includes a common quadratic \((a +b)^2\).
Then you can cancel (a + b) from both the numerator and the denominator; Quantity A is really just 6(a + b). The quantities are equal.
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Re: a ≠ –b
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06 Sep 2021, 10:16
06 Sep 2021, 10:16
2
sandy wrote:
a ≠ –b
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.
Quantity A |
Quantity B |
\(\frac{6a^2+12ab+6b^2}{(a+b)}\) |
\(6(a+b)\) |
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.
Drill 1
Question: 5
Page: 511
Question: 5
Page: 511
Given:
QUANTITY A: \(\frac{6a^2+12ab+6b^2}{(a+b)}\)
QUANTITY B: \(6(a+b)\)
First factor out the 6 from numerator in Quantity A to get:
QUANTITY A: \(\frac{6(a^2+2ab+b^2)}{(a+b)}\)
QUANTITY B: \(6(a+b)\)
Now factor quadratic in Quantity A to get:
QUANTITY A: \(\frac{6(a+b)(a+b)}{(a+b)}\)
QUANTITY B: \(6(a+b)\)
The \((a+b)\) terms cancel out in the denominator and numerator in Quantity A to get:
QUANTITY A: \(6(a+b)\)
QUANTITY B: \(6(a+b)\)
Answer: C
