2/4 quadrant multiplier theory

[David MOYLAN]

Okay, just sitting here thinking about something.
A 2 quadrant multiplier is essentially a VCA right?
And a 4 quadrant works similarly except that if the
control signal goes negative the polarity of the
signal is reversed (with respect to + control signals).
Would it be possible to get similar results by using
a Voltage Controlled Mixer mixing 2 signals 180 degrees
out of phase.  Assuming a certain bias added to the 
"control" signal, at 0 input we'd have 0 output (equal
mix of signal and inverted signal), if the control
swings positive, we get more straight signal, if it 
swings negative, we get more inverted signal.  Am I 
missing anything?  Thanks.  dave moylan