When our expedition took place in Asia, as you yourselves know refers to a military campaign waged somewhere in southwestern Asia. Most probably it is a reference to the action described briefly in 3 Macc 1.1-5.

It was brought to conclusion, according to plan means the fighting in Asia was successful, as they intended it to be.

By the gods’ deliberate alliance with us in battle: Ptolemy attributes his success to the help of the Greek gods.

Here are models for this verse:

• In fact, you know [or, You are aware, of course,] that the fighting in Asia was successful just as we planned, because the gods were definitely helping us.

• You know, of course, that the fighting in Asia was successful, just as we planned, because the gods certainly helped us in battle [or, were certainly on our side].

Quoted with permission from Bullard, Roger A. and Hatton, Howard A. A Handbook on 3-4 Maccabees. (UBS Helps for Translators). Miami: UBS, 2018. For this and other handbooks for translators see here.