Since the square of any number is always positive, \(b^2 > 0\)
Since \(b^2c < 0\), or a positive number * c = negative number, that means that c must be a negative number.
\(abc > 0\), so abc is a positive number.
abc = ab * (negative number) = positive number
That means that ab must be a negative number, since the product of two negative numbers is positive.
Therefore, ab < 0, so Quantity B is greater.

To demonstrate, say that \(a = 1\), \(b = -1\), and \(c = -2\).
\(b^2c = (-1)^2(-2) = -2 < 0\)
\(abc = (1)(-1)(-2) = 2 > 0\)
\(ab = (1)(-1) = -1 < 0\)

OR \(a = -1\), \(b = 1\), and \(c = -2\).
\(b^2c = (1)^2(-2) = -2 < 0\)
\(abc = (-1)(1)(-2) = 2 > 0\)
\(ab = (-1)(1) = -1 < 0\)