Sub connected to amp verses speaker

The essence of it is:

you want to remove the low frequencies from BOTH the amp AND the main speakers.

Then the amp has an easier job (making bass needs the most power). Then the speaker’s drivers do not need to make low bass, letting them do a better job of the upper bass and everything else.

SO: preamp to self-powered sub: Sub(s) grab the lows prior to the amp (you adjust sub’s volume and crossover point (how much bass it takes for itself).

Sub to amp, the amp now does not have to make the frequencies the Sub grabbed.

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Amp speaker wires to sub, sub speaker wires to speakers, gives the speakers a break, but not the amp which is still making all frequencies.

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preamp to self-powered sub, back to amp allows a less powerful amp for the front mains:, smaller size; power; cost; greater placement options.

This is a good way to try tubes

Your trusted source told you wrong!

 You can either run your amplifier connections to the main speakers and then run another set of speaker cables to the subwoofer. Alternatively, you can either wire from the amplifier to the subwoofer and then jump off to your main speakers, or vice versa. You can go to the speakers from the amplifier and then from the main left and right speakers, and jumper to the subwoofer. In any case, connect both the left and right speaker outputs wherever they’re coming from to the input of the subwoofer amp.

There are several reasons, but control of where the sub rolls in and the main speakers roll off is probably the most important.  Also, it Depends on the subwoofer. Rel, a very popular company,  is designed to run off your amplifiers speaker outs and even comes with a cable just for that purpose. SVS, another popular company runs off of your adjustable preamp outputs.

All the best.