\(xy > 0\)

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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Sandy
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Explanation

the terms in Quantity A:
\((2x - y)(x + 4y) = 2x^2 + 8xy - xy - 4y^2 = 2x^2 + 7xy - 4y2\)

Since \(2x^2\) and \(-4y^2\) appear in both quantities, eliminate them.

Quantity A is now equal to 7xy and Quantity B is now equal to 8xy.

Because xy > 0, Quantity B is greater. (Don’t assume! If xy were zero, the two quantities would have been equal. If xy were negative, Quantity A would have been greater.)
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Sandy
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